STRONG-FIELD IONIZATION STUDIES OF HOMO- AND …

The Pennsylvania State University

The Graduate School

Eberly College of Science

STRONG-FIELD IONIZATION STUDIES OF HOMO- AND HETEROGENEOUS

TRANSITION METAL CLUSTERS

A Dissertation in

Chemistry

by

Daniel Edward Blumling

© 2009 Daniel Edward Blumling

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

December 2009

The dissertation of Daniel Edward Blumling was reviewed and approved* by the

following:

A. Welford Castleman, Jr.

Eberly Family Distinguished Chair in Science

Evan Pugh Professor of Chemistry and Physics

Thesis Advisor

Chair of Committee

James B. Anderson

Evan Pugh Professor of Chemistry and Physics

Karl T. Mueller

Professor of Chemistry

Robert Santoro

George L. Guillet Professor of Mechanical Engineering

Director of the Propulsion Engineering Research Center

Barbara J. Garrison

Professor of Chemistry

Head of the Department of Chemistry

*Signatures are on file in the Graduate School

iii

ABSTRACT

The interaction of intense electric fields with clusters has been an active area of

research following the observation of the first laser-induced Coulomb explosion of a

cluster in 1994. The research reported in this dissertation focuses on the strong-field

ionization behavior of small clusters composed of early transition metals, carbon, and

oxygen. Specifically, several Group IV, V, and VI transition metals have been bonded

either with themselves or in combination with sufficient oxygen or carbon atoms to form

a variety of small (fewer than 40 atoms) cluster species. Following the ionization of

these clusters via ultrashort laser pulses, observations are made regarding the ion

products, their energies, and the mechanisms which led to their creation. Time-of-flight

mass spectrometry is used to obtain data on the resulting species.

A general overview of laser-matter interactions and strong-field ionization is

provided in Chapter 1. The experimental apparati, including a colliding-pulse, mode-

locked dye laser, a laser ablation cluster source, and a reflectron time-of-flight mass

spectrometer, are described in Chapter 2. In Chapter 3, strong-field ionization studies of

transition metal (Ti, V, Cr, Nb, or Ta) oxide clusters are presented. Trends relating the

reported ionization energies of the component atoms and the observed maximum charge

states of the ions are reported. Discussion is offered relating the observed ionization

behavior to the most commonly considered enhanced ionization mechanisms from the

literature. The results of the strong-field ionization of pure transition metal clusters are

then reported in Chapter 4 and this data is compared to that obtained for the transition

metal oxide species. The maximum ionization states for the metal atoms in both the

homo- and heteronuclear systems were identical and the ramifications of this

phenomenon with regard to ionization dynamics are discussed. Finally, Chapter 5

contains data and analysis of the strong-field ionization and subsequent Coulomb

explosion of transition metal carbide clusters. Remarkably, the maximum charge states

for each constituent transition metal atom in both types of heteronuclear system, as well

as the pure metal clusters, were identical following ultrashort laser ionization.

iv

Studies of these systems satisfy several specific goals in laser-induced Coulomb

explosion research. First, the theory regarding strong-field ionization of clusters in this

size regime is somewhat lacking, and the reported ionization mechanisms are complex

and not unambiguous. The additional information regarding experimental values for

maximum charge states with respect to not only cluster composition but also the ionizing

laser conditions should prove beneficial to the advancement of theoretical models. In that

same vein, studies of heteronuclear, covalently-bound clusters have never been reported

in the literature, and thus the information garnered from these experiments provides a

perspective as yet unavailable. Further, by systematically controlling the elemental

composition of our cluster distributions, we have been able to observe trends in the

ionization behavior with respect to the overall cluster composition and its effects on the

individual atomic species contained with these species.

v

TABLE OF CONTENTS

LIST OF FIGURES ................................................................................................. viii

LIST OF TABLES .................................................................................................. xvii

ACKNOWLEDGEMENTS ..................................................................................... xviiii

Chapter 1 Introduction: Clusters and Laser-Matter Interactions ............................... 1

1.1 Clusters ....................................................................................................... 1

1.2 Atoms in Strong Electric Fields................................................................... 3

1.2.1 Multiphoton Ionization (MPI) ........................................................... 3

1.2.2 Tunneling Ionization (TI) .................................................................. 5

1.2.3 The Keldysh (or Adiabatic) Parameter (γ) ......................................... 9

1.2.4 Predicting Ionization Rates................................................................ 11

1.3 Enhanced Ionization Mechanisms ............................................................... 12

1.3.1 Ionization Ignition Mechanism (IIM) ................................................ 13

1.3.2 Charge Resonance Enhanced Ionization (CREI) ................................ 15

1.3.3 Coherent Electron Motion Mechanism (CEMM) or Nanoplasma

Model ................................................................................................. 19

1.4 References: ................................................................................................. 22

Chapter 2 Experimental Setup: Apparati and Techniques ........................................ 24

2.1 Cluster Source ............................................................................................ 25

2.2 Femtosecond Laser Facility......................................................................... 28

2.2.1 Colliding Pulse Mode-locked (CPM) Dye Laser ................................ 28

2.2.2 Bowtie Amplifier .............................................................................. 30

2.2.3 Bethune Cell Amplification ............................................................... 32

2.3 Time-of-Flight Mass Spectrometer (TOF-MS) ............................................ 34

2.3.1 Time-of-Flight Extraction Region ..................................................... 34

2.3.1.1 Kinetic Energy Release (KER) Measurements ......................... 37

2.3.2 Deflector Plate .................................................................................. 40

2.3.3 Einzel Lens ....................................................................................... 42

2.3.4 Detection: Microchannel Plate Detector ............................................ 44

2.4 Vacuum Systems ........................................................................................ 45

vi

2.5 References: ................................................................................................. 48

Chapter 3 Strong Field Ionization Studies of Transition Metal Oxide Clusters ........ 49

3.1 Introduction ................................................................................................ 49

3.2 Experimental............................................................................................... 51

3.3 Results ........................................................................................................ 53

3.3.1 Titanium Oxide Clusters ................................................................... 53

3.3.2 Vanadium Oxide Clusters ................................................................. 57

3.3.3 Chromium Oxide Clusters ................................................................. 60

3.3.4 Niobium Oxide Clusters .................................................................... 62

3.3.5 Tantalum Oxide Clusters ................................................................... 65

3.4 Analysis and Discussion ............................................................................. 67

3.5 Conclusions ................................................................................................ 82

3.6 References: ................................................................................................. 83

Chapter 4 Strong Field Ionization Studies of Homogenous Transition Metal

Clusters ............................................................................................................ 85

4.1 Introduction ................................................................................................ 85

4.2 Experimental Details ................................................................................... 88

4.3 Results ........................................................................................................ 93

4.3.1 Pure Niobium Cluster Studies ........................................................... 94

4.3.2 Pure Tantalum Cluster Studies .......................................................... 96

4.4 Analysis and Discussion ............................................................................. 100

4.5 Conclusions ................................................................................................ 107

4.6 References .................................................................................................. 109

Chapter 5 Strong-Field Ionization Studies of Transition Metal Carbide Clusters ..... 111

5.1 Introduction ................................................................................................ 111

5.2 Experimental Details ................................................................................... 114

5.3 Results and Discussion................................................................................ 115

5.3.1 Titanium Carbide Clusters ................................................................. 116

5.3.2 Vanadium Carbide Clusters ............................................................... 120

5.3.3 Chromium Carbide Clusters .............................................................. 123

5.3.4 Niobium Carbide Clusters ................................................................. 125

5.3.5 Tantalum Carbide Clusters ................................................................ 129

vii

5.4 Conclusions ................................................................................................ 137

5.5 References .................................................................................................. 139

Appendix A Useful Equations................................................................................. 141

viii

LIST OF FIGURES

1-1: Schematic of multiphoton ionization (MPI) (a) and above threshold

ionization (ATI) (b). ......................................................................................... 4

1-2: Schematic depicting MPI (for reference) (a) and the deformation of the

electron potential well (b) which can lead to tunnel ionization when the

system is subjected to a strong static external electric field (E). Rather than

vertically escaping the potential well (as in MPI), the electron has a finite

probability of tunneling through the suppressed barrier and entering the

continuum. ........................................................................................................ 6

1-3: Schematic depicting the effects of neighboring ions within a diatomic system

which may lead to the ionization ignition mechanism. Higher charges result

in larger Coulomb attraction between an ion and neighboring electron which

reduces the energy required for removal of that electron. This behavior is

represented by the lowering of the potential barrier in the direction of the

neighboring ion. ................................................................................................ 13

1-4: Schematic representation of the charge resonance enhanced ionization

mechanism as it applies to a diatomic system in the presence of a static

electric field. As the distance between the two atomic species grows (r’r

’’’)

the interaction between the potential wells changes accordingly. At small

internuclear distances, electrons may transfer between the two atomic cores

but remain bound within the dimer (inner ionization). At r’’, the interatomic

distance is such that electrons can escape the potential well (via tunneling or

over the barrier ionization) on the left and then directly escape to vacuum

(outer ionize). Finally, at large interatomic distances (r’’’

), electrons in the

left well remained bound there, while ionization may still proceed from the

right potential well. Thus, ionization becomes enhanced at the intermediate

distance due to the simultaneous and cooperative suppression of the inner and

outer potential barriers. ..................................................................................... 17

1-5: Schematic to illustrate the nature of a Jellium-type cluster and the onset of a

cluster plasmon. The nuclei and valence electrons which comprise the cluster

may be thought of as diffuse positively- (a) and negatively-charged (b)

clouds. The interaction between the delocalized electron density and the

inner metallic ion cores results is a dynamic one and collective and coherent

oscillatory behavior can be induced by an external electric field (c). The

cartoon of the waveform is misleading as the size of the target cluster should

be sufficiently smaller than the laser pulse that the entire cluster experiences

an identical influence from the field. The cluster’s frequency is unique to the

ix

size, dimensions, composition, etc. of a particular cluster. See text for more

details. .............................................................................................................. 20

2-1: A schematic representation of the cluster source and mass spectrometer.

Following creation in the laser vaporization source (a), the clusters traveled a

short distance until they were irradiated with an ultrashort pulse of light as

they passed between the electrostatic grids which constitute the Wiley-

McLaren extraction region (b). Based on the electric field parameters of the

extraction region, any cationic products resulting from the laser ionization

event were directed into the mass spectrometer, wherein they encountered a

beam-steering deflector plate (c) and an Einzel lens (d) prior to being

detected at the microchannel plate (MCP) detector (e) in the short field-free

region experiments. For the long field-free region experiments, the cationic

products bypassed the detector located at (e) and traveled to the reflectron

assembly at (f) where they were turned back towards the secondary MCP

detector at (g). .................................................................................................. 25

2-2: Detailed schematic of the laser vaporization source used in these

experiments. Briefly, reactant/clustering gases were introduced via the inlet

at (a) whereupon pulses of the gas were created using the solenoid pulsed-

nozzle (b). At a certain time during each gas pulse, the second harmonic

(532nm) of an Nd:YAG laser was directed into the source (c) where it ablated

a target metal rod (d) which was simultaneously being rotated and translated

to ensure a “clean” spot on the rod for each subsequent ablation event. The

position of this rod was maintained via a spring-loaded ball bearing guide (e)

with the intent of minimizing changes in interior source dimensions in case of

rod imbalance. Following creation of the metal-gas plasma, the ionized

materials were directed into the waiting room (f) prior to escaping the source

via the expansion nozzle (g) and entering into the ionization region of the

mass spectrometer............................................................................................. 26

2-3: Schematic overview of the CPM dye laser and subsequent amplification

apparati. Note the compression gratings which, when present, recompressed

the beam to yield pulses of ~100fs in width. Without the gratings, 350fs

pulses were attained. The recommended power distributions for the Nd:YAG

amplification system have been provided. Prior to entering the TOF-MS

within the vacuum chamber, the femtosecond pulse beam was focused down

to intensities above 1014

W/cm2 via a 50cm focal lens. ....................................... 29

2-4: Schematic depiction of the extraction region (a), deflector plate (b), and

Einzel lens (c) assemblies including typical operational voltages. As the

neutral cluster beam enters the region between the repeller (at +4kV) and

extractor (+2kV) plates, its constituents would be irradiated with an

ultrashort, intense laser pulse (not shown) and subsequently undergo SFI.

x

The solid blue line represents a simplified view of the assumed path taken by

the resulting cations. Whereas their residual downward momentum might

normally force the majority of ions out of the range of detection in the mass

spectrometer, the deflector plate, typical held at a static voltage of 80-160V,

compensates for the undesired motion and directs the majority of the products

towards the detector. Simultaneously, the deflector plate serves to push any

ionic products resulting from SFI of background contaminants (dashed red

line) off-axis and reduce their significance in the mass spectra (extended path

extrapolated for illustration purposes). .............................................................. 35

2-5: An ensemble of mass spectra obtained by varying the location of the laser’s

focal point. In doing so, the electric field strength which the target species

were exposed to was also changed accordingly. The furthest point on the z-

axis represents the spectrum which contains ions created at the least focused

(and therefore least intense) part of the laser beam. There was little to no

evidence of multiply-charged species while most of the clusters become

singly-ionized and arrive at the detector intact. As the focus was

incrementally tightened and the clusters were exposed to higher laser

intensities (towards zero on the z-axis), the larger clusters began to fragment

and multiply-charged ions became evident in the mass spectrum. The

spectrum taken at the highest intensity for this experiment does not represent

the maximum available intensity, as this figure is provided for illustrative

purposes alone. At the maximum field intensity, the multiply charged ion

signal dominated the spectrum and singly charged polyatomic species were

rarely observed in any appreciable amount. The small throughput orifice in

the extraction plate of the TOF assembled aided in narrowing the observed

species to those exposed to similar field intensities. .......................................... 36

2-6: Screenshot from a SIMION® simulation of a Coulomb explosion event

within the confines of an ion extraction apparatus similar to the one

employed in these experiments. Although this is an idealized situation, it is

clear that despite the fact that ions may be ejected with vectors in any

direction, only those particles with a direction of propagation which is

collinear (or very nearly so, at least) with the axis of the mass spectrometer

have the opportunity to be detected. .................................................................. 37

2-7: Demonstration of applications of kinetic energy release (KER) values. The

solid black line represents the overall spectrum obtained via SFI of transition

metal oxide clusters and any background, unclustered species in the path of

the laser. The dashed red line shows several of the species commonly

observed in the background of our experiments while the solid green line is a

subtracted spectrum which results when the signal from the background is

subtracted from the total spectrum. In this way, the KER of many species

was obtained more easily and accurately. As noted, the hydrocarbon ion

xi

result from the SFI of background vacuum pump oil and serve as an

illuminating demonstration that the background oil ionization increases in

intensity during the ionization of the target cluster species. This has been

attributed to secondary electron impact ionization and makes it impossible to

completely eliminate background contaminant signal from the observed mass

spectra. ............................................................................................................. 40

2-8: Mass spectrum of the singly-ionized background contamination omnipresent

in the vacuum chamber. This spectrum was obtained by defocusing the

femtosecond pulse train to allow for ionization without Coulomb explosion.

The inset spectrum contains several labels for the more intense peaks and

demonstrates the abundance of species resulting from the fragmentation of

large hydrocarbons. It should be noted that this spectrum was obtained with

the deflector plate held at a grounded potential to allow the observation of the

entire population. .............................................................................................. 43

2-9: Experimental mass spectrum of the multiply charged ions which result from

the laser-induced strong-field ionization of background contamination. The

hydrocarbon-based pump oil [(CH2)n where 20<n<40] employed in our

vacuum system is the most likely source of the majority of this

contamination. Additional ions result from the SFI of water and nitrogen

molecules. Unfortunately, simple background subtraction techniques were

typically insufficient for the elimination of this signal due to a noticeable

increase in the intensity of the ionized background species in the presence of

the target cluster systems. This has been attributed to electron- and ion-

impact ionization of the background species resulting from collisions with the

highly energetic particles ejected during the Coulomb explosion of the parent

clusters. ............................................................................................................ 44

3-1: Cationic mass spectrum of titanium oxide clusters. ........................................... 54

3-2: Mass spectrum of the highly charged ionic species which result from the

Coulomb explosion of titanium oxide clusters. Note the maximum observed

charge states for the target species are Ti+10

and O+6

. The isotope distribution

for titanium is clearly seen for charge states +1 thru +5. Any areas in which

mass degeneracies between target species and background contributions are

noted. See text for details. ................................................................................ 56

3-3: Typical cationic mass spectrum for vanadium oxide clusters. ........................... 58


Coulomb explosion of vanadium oxide clusters. Note the maximum

observed charge states for the target species are V+9

and O+6

. The spectrum

has been truncated slightly to focus on the maximum observable charge states

of the metal species. .......................................................................................... 59

xii

3-5: Typical cationic mass spectrum for chromium oxide clusters. ........................... 61


Coulomb explosion of chromium oxide clusters. Note the maximum

observed charge states for the target species are Cr+8

and O+6

. As discussed

in the text, the Cr+9

ion may also be present, but masked due to a near mass

degeneracy with C+2

. ........................................................................................ 62

3-7: Typical neutral mass spectrum for small niobium oxide clusters. This

spectrum was obtained via the defocused ultrafast ionization laser. The CPM

pulse was typically defocused by ~3cm, resulting in intensities of ~1x1012

W/cm2. ............................................................................................................. 63


Coulomb explosion of niobium oxide clusters. Note the maximum observed

charge states for the target species are Nb+11

and O+6

. ....................................... 64

3-9: Typical neutral mass spectrum for tantalum oxide clusters. Again, the CPM

was defocused to obtain an approximate intensity of 1012

W/cm2. ..................... 65


strong field ionization (I~1015

W/cm2) of tantalum oxide clusters. Note the

maximum observed charge states for the target species are Ta+11

and O+6

.

Higher charge states of tantalum may be present but masked by the mass-

degeneracies with the background contaminants. See text for details................ 66

3-11: Graphical depiction of the reported sequential ionization energies for the

Group IV metals and oxygen. The energies which correspond to the

maximum observed charge state for each metal are highlighted and relevant

energies are provided. ....................................................................................... 70

3-12: Graphical depiction of the ionization energies for the Group Vb metals

studied in this work. The energy necessary to create the Nb+11

ion is assumed

based on the arguments provided in the text. ..................................................... 72

3-13: Normalized ion populations for the multiply charged species resulting from

strong-field ionization via a 350fs pulse (“long pulse” – black bars on the

left) or a 100fs pulse (“short pulse” – red bars on the right) of small niobium

oxide clusters. ................................................................................................... 77

3-14: Comparative, normalized distribution of small (lower, black line, Series 1)

niobium oxide clusters plotted with the heavier distribution (upper, red line,

Series 2). .......................................................................................................... 78

xiii

3-15: Kinetic energy release (KER) values for selected niobium and oxygen

atoms to demonstrate cluster expansion during ionization via 100fs vs. 350fs

pulse widths. ..................................................................................................... 79

4-1: Illustrative depiction of the LaVa source change required for the creation of

pure metal clusters. The source used in previous experiments (a) remained

primarily the same, with the exception of the implementation of a different

expansion nozzle (b). The new nozzle was slightly longer (38.5mm) and

much narrower (1.5mm) throughout its entire length. This nozzle also

decreased the size of the waiting room, increased the pressure inside the

source, and aided in removing additional energy from the system to stabilize

the pure metal clusters. Several important components of the source are

labeled for clarity. ............................................................................................. 93

4-2: Typical cluster distribution for the neutral homogeneous niobium species.

Note that this spectrum was obtained via the defocused CPM beam by

translating the focusing lens approximately 3cm away from the maximum

focus position, thus reducing the laser intensity to ~1012

W/cm2 thus

minimizing multiple ionization events to enhance single ionization. The

figure is a combination of two spectra to enable a complete depiction of the

entire cluster distribution. ................................................................................. 95

4-3: Mass spectrum resulting from the SFI of neutral homogeneous niobium

clusters via a 100fs laser pulse. Note the maximum observable charge state is

the Nb+11

ion. .................................................................................................... 97

4-4: Mass spectrum resulting from the SFI of neutral homogeneous niobium


the Nb+11

ion. .................................................................................................... 97

4-5: Typical cluster distribution for the neutral homogeneous tantalum species.

Note that this spectrum was obtained via the defocused CPM beam and is a

combination of two spectra to enable a complete depiction of the entire

cluster distribution. ........................................................................................... 98

4-6: Mass spectrum resulting from the SFI of neutral homogeneous tantalum


the Ta+11

ion. .................................................................................................... 99

4-7: Mass spectrum resulting from the SFI of neutral homogeneous tantalum


the Ta+11

ion. .................................................................................................... 99

xiv

5-1: Mass spectrum of the multiply charged ion species which resulted from the

SFI (I~1015

W/cm2) of small titanium carbide clusters. Note the MOCS of

Ti+10

and the clear evidence of C+4

in the spectrum. .......................................... 117

5-2: Reported ionization energy values [16] for the species studied in this chapter.

The energy associated with the MOCS observed in each specific study is

highlighted in bold while a box has been provided to guide the eye to the

narrow range of energies corresponding to the MOCS values. All energies

are in electronvolts............................................................................................ 118

5-3: Cluster distribution for neutral vanadium carbide clusters obtained via

defocused CPM with an approximate intensity of 1012

W/cm2. Note the

enhanced intensity of the Met-Car, V8C12 at mass ~551amu. The V3C8 and

V4C4 peaks are labeled as indicated in the text. ................................................. 121


SFI of small vanadium carbide clusters. The MOCS for this study was V+9

while C+4

was also easily seen. Dashed lines are provided to guide the eye

and are positioned according to the overall mass-to-charge ratio calibration

for this figure. ................................................................................................... 122


SFI of small chromium carbide clusters. Cr+8

is clearly resolved while Cr+9

is

likely present, albeit obscured by the large C+2

peak. Dashed lines

corresponding to the overall calibration line are provided to guide the eye and

demonstrate the expected overlap between C+2

and Cr+9

mass signals. .............. 124

5-6: Mass spectrum depicting a typical niobium carbide cluster distribution. ........... 126


SFI of small niobium carbide clusters. The Nb+11

ion is clearly present

(dashed lines corresponding to a mass calibration equation are provided). C+4

was also observed, although this spectrum was truncated to highlight the

metal species and thus the highly charged carbon ions are not evident. Figure

5-8 has also been provided to more clearly demonstrate the identification of

the Nb+x

(x = 58) species. .............................................................................. 127

5-8: Highly truncated mass spectrum resulting from the SFI of niobium carbide

clusters. This expanded view clearly demonstrates the presence of several

highly charged niobium species despite near mass degeneracies with several

background hydrocarbon peaks. ........................................................................ 128

5-9: Typical mass spectrum of the target tantalum carbide cluster distribution.

Mass resolution becomes decreased around 960 mass units but the observed

stoichiometry is still identifiable. ...................................................................... 130

xv


SFI of small tantalum carbide clusters. The maximum charge states of Ta+11

and C+4

are evident. .......................................................................................... 131

5-11: Theoretically calculated structures for NbxCy clusters [21]. ............................. 135

5-12: Theoretically calculated structures of several TixCy clusters [22]. ................... 136

xvi

LIST OF TABLES

3-1: Table presenting the maximum observable charge states (MOCS) resulting

from the SFI of each transition metal oxide cluster series. ................................. 68

5-1: Overall summary of the maximum observed charge states resulting from the

strong-field ionization of several transition metal oxide, carbide, and

homogenous clusters. The (+9) attributed to the chromium species is likely

present, as discussed in the text. ........................................................................ 133

xvii

ACKNOWLEDGEMENTS

Regarding the research reported in the pages of this dissertation, there are two

primary people who must be thanked. First and foremost I wish to acknowledge my

advisor, A. W. “Will” Castleman, Jr. for his support, insight, patience, and

encouragement throughout my graduate career. Secondly, I had the privilege to work

with an excellent scientist, Scott Sayres, for the majority of my time at Penn State. His

aid, humor, diligence, and creativity throughout the experimentation process proved

invaluable. In a similar vein, I’d like to thank Dr. Jason Stairs and Prof. Ken

Knappenberger for my initial introductions to gas-phase experimentation and laser

science, respectively. My research also benefitted from advice and encouragement from

Dr. Kevin Davis, Dr. Sam Peppernick, David Grove, Dr. Justin Golightly, Dr. Darren

Hydutsky, Dr. Dina Justes, Dr. Michele Kimble, and many of the other past and present

members of the Castleman Research community. I would also be remiss if I didn’t thank

Connie Smith (you made every non-science aspect of my Penn State life easier), the Penn

State electronics shop (especially Bob Crable), and many of the fine gentlemen in the

machine shop.

I was fortunate in my experience at Penn State that I not only obtained an

excellent education, but I also met some of the most wonderfully interesting friends I’ve

ever known. Many of these people became very dear to me and I’d like to acknowledge

and thank them for all they did for me, whether it was support in difficult times or a

welcome distraction from the research grind. In no particular order, thank you Adam,

Kansas, Joe, Sam, Scott, Dano, Nick, Cheryl, Melissa, Shianne, Jeff, Ellen, Dom, Ken,

Jason, Carisa, Becca, Laura, Jason, Nasty, Martin, Duane, Laurie, Dave, Erin, Nelly,

Michele, Dina, and all of the bartenders whom I’ve gotten to know at the Allen St. Grille.

Also, whenever I was in need of a break from my work (and sometimes when I wasn’t!)

my college buddies were always willing to take a trip up to visit me, so thank you Ryan,

Andy, Scott, and Dick.

xviii

I’d also like to thank my family for their support and gentle harassment

throughout the years; my parents, Robert and Georjeane, and my brothers, Alan and

Michael. Finally, last but not least, I want to acknowledge my wife Michelle. I could

never thank you enough for all you have done for me, but I promise to spend the rest of

my life trying.

This work is dedicated to my Mamaw, Jeannie Kirby, my Papaw, Maynard

“Page” Kirby, and my Grandpa, Bill Blumling.

Chapter 1

Introduction: Clusters and Laser-Matter Interactions

In 1994, the first experimental evidence of the laser-induced Coulomb explosion

of a cluster was obtained in the Castleman labs by Jeffrey Purnell, Eric Snyder, and S.

Wei [1]. Since that time, studies investigating the interaction of strong electric fields and

matter have evolved into a field of their own. The work contained in this thesis focuses

on the investigation of ionization and Coulomb explosion behaviors of small homo- and

heteronuclear transition metal clusters in strong optical fields. To date, the majority of

strong-field cluster work has been performed on systems characterized by metallic or van

der Waal’s bonding schemes. The experiments herein represent an initial foray into an as

yet unexplored region of laser-matter interactions, specifically those involving small

homo- and heteronuclear transition metal clusters. Past research has provided a wealth of

information regarding strong field science, and some of that which is well understood and

germane to this work is delineated in this introduction.

1.1 Clusters

Clusters are often described as the fifth state of matter. Studies of their properties

and applications date back to the mid-1800’s [2] and have continued to expand ever

since. They may be homo- or hetero-nuclear, composed of merely 2 atoms or possessing

nuclei numbering in the tens of thousands. Their constituent atoms may be held together

by van der Waal’s, covalent, hydrogen, ionic, or metallic bonding; their structures may be

well-defined or amorphous. The term “cluster” has been used in a wide variety of ways

to describe numerous species, and the semantic arguments regarding what actually

constitutes a cluster are manifold and unending. However, their usefulness in research,

2

both pure and applied, is undeniable. They can possess the density of a solid and the

optical transparency of a gas. Techniques exist for rapidly creating clusters with a range

of sizes, compositions, and properties, making them irreplaceable in the laboratory,

where flexibility and reproducibility are always highly desirable.

In this work, discussion will primarily be limited to heterogeneous transition

metal clusters, specifically early (Groups IV, V, and VI) transition metals doped with

oxygen or carbon. One set of experiments was also focused on studies of homonuclear

niobium and tantalum clusters. Transition metal oxide and carbide systems have been

investigated for many years due to their role in the catalysis of a variety of chemical

reactions. Further, it has been demonstrated that the reactive sites for the bulk catalytic

materials can be modeled with clusters of specific size, shape, and composition, making

clusters an important tool in the development of better catalysts. As such, these cluster

systems have received a substantial amount of attention and many of the smaller (<20

atoms) clusters are well characterized. See Refs 3, 4 -7 for useful reviews.

Of the many unique characteristics possessed by transition metal clusters, perhaps

one of the most germane to this work is the open-shell electron nature of the species. The

multiple valence electrons which are a result of the incomplete d-shell in transition metals

lead to several interesting properties, one of which is the suppression of strong field

ionization rates [8]. Unlike noble metal clusters (noble metal atoms possess a full d10

shell), transition metal clusters do not typically display jellium shell closings in which the

combined valence electrons from each atom within the cluster interact to create virtual

shell closings which can enable the entire cluster to be treated as a large single atom [7].

Further, when clustered with oxygen or carbon atoms, transition metals form covalent

bonds within the cluster. The electronegativity of the companion oxygen and carbon

atoms dictates that many of the localized d-electrons of the transition metals will be

concentrated near the nonmetal species, creating polar covalent bonds. In the two non-

substituted transition metal clusters discussed in this work, metallic bonding dominates.

3

1.2 Atoms in Strong Electric Fields

With the creation of the first laser, scientists gained a tool which allowed them to

study the interactions between matter and energy (in the form of light) in an exciting new

manner. Einstein’s photoelectric effect could be controlled and manipulated in ways

never before possible. Future development of ultrashort laser pulses gave rise to studies

of matter interacting not only with photons with discrete quanta of energy, but with the

overall electric field created by an electromagnetic wave. In 1982, shortly after the

development of the first laser system capable of delivering sub-picosecond pulses of

light, it was discovered that intense, linearly polarized radiation impinging upon a gas-

phase system gave rise to a large population of multiply charged ions [9]. In the present

section, the basics of these strong-field interactions are reviewed with a focus on the

ionization behavior of atoms exposed to the strong electric fields created by ultrashort

laser pulses.

Given identical target species, various ionization mechanisms can dominate the

dynamics of a system. The prevailing process is directly related to the intensity of the

incident laser pulse and its corresponding electric field strength. Using the hydrogen

atom (ionization potential = 13.6eV) as a benchmark example, multiphoton ionization

(MPI) dominates at lower intensities (<1014

W/cm2) whereas over-the-barrier ionization

(OTBI) can only be reached when the electric field of the laser approaches relativistic

levels (>1018

W/cm2), with tunnel ionization (TI) being the main process at ranges

between those limits [10].

1.2.1 Multiphoton Ionization (MPI)

In its most simple definition, ionization is the process of creating an ion by the

addition or subtraction of an electron from a species. For the sake of clarity, this section

will only be referring to ionization in the sense of electron loss; i.e. the creation of cations

from a neutral species. Photoionization is the process by which an electron gains enough

4

energy from a photon to surpass the attraction it feels to a nucleus and escape into the

vacuum. This attraction is commonly referred to as the system’s ionization potential (IP).

Multiphoton ionization, therefore, refers to a scenario in which multiple photons of

discrete energy are required to provide enough energy to ionize a system. MPI is a

nonlinear process, and thus it was not until the invention of the laser that observations of

this behavior were possible. In fact, the first experimental observations of multiphoton

excitation were published immediately after the invention of the laser [11], in 1961, and

the first MPI experiment followed soon after in 1965 [12]. This first MPI experiment

was performed by Voronov and Delone and involved the ionization of rare gas atoms.

The primary concept in understanding MPI is the relationship between photon

energy and ionization potential, which is depicted in Figure 1-1 (a). Each photon

absorbed by the active electron adds a discrete amount of energy (hν) and when enough

photons (n) are simultaneously absorbed, the electron may be ionized out of a potential

well which required more energy than one photon alone could provide. Any absorbed

energy which exceeds that which was required for ionization is harvested as kinetic

1-1: Schematic of multiphoton ionization (MPI) (a) and above threshold ionization (ATI) (b).

5

energy (KE); an incredibly useful phenomenon which is the basis for many spectroscopic

techniques including velocity map imaging, photoelectron spectroscopy, etc. This

relationship is depicted in Equation 1-1,

Also shown in Figure 1-1(b) is the process which occurs specifically when an electron

absorbs more photons than necessary to escape the potential well; known as above

threshold ionization (ATI). In this scenario, Eqn. 1-1 changes slightly to the form KE =

(n+x)hν – IP, where x is the number of additional photons absorbed.

1.2.2 Tunneling Ionization (TI)

MPI is the dominating ionization process up to the point at which the strength of

the electric field associated with a laser pulse is large enough to be comparable to that of

the attractive forces felt between the electron and the nuclear core of an atom. The

discrete energies of each individual photon are no longer as significant as they are in

MPI. At these intensities, the laser’s electric field can lower the potential barrier for

ionization to the point at which an electron has a significant probability for tunneling

through the suppressed barrier and escaping the system. Specifically, tunneling refers to

a quantum mechanical phenomenon in which there is a finite probability that a particle

can exist in a state which is energetically inaccessible based on classical mechanics. This

process is referred to as tunneling ionization (TI) and it is a dominant mechanism

influencing the initial ionization events in the experiments described in this thesis.

Often, this concept is demonstrated using the particle-in-a-box model with walls

of finite thickness. Again, the tunneling phenomenon has no basis in classical physics

and is thus treated purely quantum mechanically, mainly because the wavefunction used

to describe an electron is pivotal in understanding the tunneling concept. Traditionally,

. 1-1

6

the time-independent Schrödinger equation is used to define an electron wave-function

and its probability for existing beyond a classical energy barrier. Treatments such as this

may be found in most Physical Chemistry textbooks and thus are omitted here.

Tunneling probability is based on several factors, two of which are the mass of

the target particle and the thickness of the potential barrier. In the studies discussed in

this thesis, the particles involved in the tunneling events are electrons and thus the masses

being dealt with are sufficiently small enough to give an appreciable probability for

tunneling. Further, the external electric field provided by the incident laser pulse serves

the function of decreasing the thickness and height of the potential barrier, increasing the

probability of a tunneling event. The following explanation attempts to hybridize an

understanding of the classical behavior of an electric field influencing a charged particle

with the probability of a quantum mechanical tunneling phenomenon.

Consider the hydrogen atom, composed of one proton and one electron, with an

ionization potential (or electron binding energy) of 13.6eV. The value of this binding

energy stems primarily from the attractive Coulomb potential that exists between the

1-2: Schematic depicting MPI (for reference) (a) and the deformation of the electron potential well (b)

which can lead to tunnel ionization when the system is subjected to a strong static external electric field

(E). Rather than vertically escaping the potential well (as in MPI), the electron has a finite probability of

tunneling through the suppressed barrier and entering the continuum.

7

positively charged nucleus and the negatively charged electron. In its most basic form,

the Coulomb potential between two particles can be described as the electric force (F)

between two charged particles based on the value of those charges (Q1, Q2) and the

distance between them, d,

The resistance to this force as a result of the surrounding environment is accounted for

via the Coulomb’s Law constant, k, which has a value of 9.0x109 Nm

-2 in air.

Upon reaching an intensity at which the electric field of a laser pulse becomes

substantial enough to influence the path of an electron, the initial probability distribution

for that electron is altered. This phenomenon is known as a Stark shift and it is the

complementary mechanism to the Zeeman shift associated with external influences from

a magnetic field. By shifting its position the electron probability density is thus localized

either closer to or further from the relatively unaffected, significantly more massive

nucleus (reminiscent of the Born-Oppenheimer approximation). The Stark shift thus

represents a change in the value of the Coulomb potential between the two which alters

the amount of energy necessary to ionize the electron.

Returning momentarily to a quantum mechanical picture, the influence of the

external electric field is essentially making the walls of the potential well thinner by

lowering the difference in energy between the electron and the far side of the potential

barrier, and so increasing the probability of a tunneling event. Taken to an extreme, once

the strength of the electric field is substantially stronger than the binding energy of the

electron, the system can be viewed classically wherein there is no barrier to ionization

and tunneling considerations become unimportant. This is an interesting concept in that

it can be used to determine the critical external field strength (Ec) required to classically

remove an electron via a simple equation

. 1-2

1-3

8

where Z is the atomic number and e is the charge of an electron. Calculating the

corresponding critical laser intensity (Ic) for this field strength is performed with

Equation 1-4,

This process is known as barrier-suppression ionization (BSI) and it is likely manifested

in the experiments contained within this work; specifically for the first few ionization

events in a system. The onset of this type of behavior is often referred to as the “classical

threshold”.

As alluded to above, the magnitude of the electric field’s influence on the electron

is vital to this change in probability as it controls the amount of Stark shifting and energy

donation to the electron. This electric field strength is also known as the ponderomotive

potential, Up,

or its more convenient formulation,

where we consider e (1.602x10-19

Coulombs) and m, the mass of an electron (9.109x10-31

kg) as a single constant, while exchanging frequency for wavelength (λ) (in microns) and

electric field amplitude (ε) with laser intensity (I) (in W/cm2).

Based on the model delineated above, it is clear that the regime in which

tunneling is the dominant ionization mechanism is relatively small and its rate increases

dramatically within that limit; i.e. the conditions required for tunneling to occur dictate a

small window of probability. Specifically, tunneling should only be the major route for

ionization when the ponderomotive potential of the laser’s electric field is roughly

equivalent to the ionization energy of the electron. This characteristic has been discussed

before and is well reviewed by J H Posthumus [13] in his seminal article on the dynamics

of small molecules in strong electric fields. Therein he also notes that the laser intensity

. 1-4

2

22

4

m

eU p 1-5

2141033.9 IU p

1-6

9

required for tunneling ionization is often very close to the intensity associated with

classical behavior, and thus this intensity will be highly dependent upon experimental

parameters and, interestingly, therefore cannot be treated as a tangible parameter in and

of itself.

1.2.3 The Keldysh (or Adiabatic) Parameter (γ)

From the above discussions, it should be apparent that the intensity of the incident

laser pulse, along with the ionization potential of a system, plays a nontrivial role in

determining the subsequent ionization mechanism. In 1964, Keldysh realized the

importance of characterizing this transition and published his seminal work on the subject

[10]. In that publication he proposed a unitless adiabatic parameter, more commonly

referred to as the Keldysh parameter (γ), which is directly related to the strength of the

incident electric field and the ionization potential of its target. The ratio between these

two values indicates the ionization phenomenon which is most likely to occur. A recent

review of this work, and its developments over the last 40 years, may be found in [14].

In light of that publication, the Keldysh parameter, its origins and uses, will only be

briefly explained herein from an experimentalist’s point of reference.

It is important to note that the Keldysh parameter only accounts for adiabatic

electron dynamics and, in the simple form provided herein, does not extend to systems in

which electron excitation dynamics within the potential well are possible. In strong-field

ionization, a system is described as adiabatic if the electron tunneling ionization

dynamics occur on a much shorter time scale than the periodic oscillations of the incident

electric field. This is also referred to as the “quasi-static approximation” in which the

frequency of the electric field is significantly slow compared to the rate at which

tunneling ionization occurs. Several common scenarios exist in which these

approximations no longer hold true. For example, larger polyatomic systems containing

higher numbers of electronic degrees of freedom can serve to slow the electronic

transition rates sufficiently that the approximation is no longer valid. Further, if the

10

wavelength of the incident electric field is short enough, the tunneling transition may no

longer proceed fast enough with respect to the oscillatory frequency of the field.

Situations such as these promote the occurrence of additional electron dynamics within

the potential well which are not accounted for by the adiabatic Keldysh parameter.

However, the concepts on which the parameter is based are somewhat central to the

realm of strong-field ionization and therefore will be described below.

The Keldysh parameter relates the ionization potential of the target chromophore

to the strength of the incident electric field. If the electric field strength is relatively low,

then γ >>1 and multiphoton ionization dominates. However, if the strength of the electric

field is sufficiently high, γ << 1, indicates over the barrier strong field ionization. The

regime in which 1>γ>0 represents the scenario in which tunneling ionization is most

likely to occur. It is important to note that these ranges cannot be treated as exact

thresholds; in fact, the probability of overlapping routes to ionization existing within the

same system is quite high for the experiments reported here as well as throughout the

published work of others.

The original form of the relationship that provides the value for γ is shown in

Equation 1-7

In this original equation, the frequency of the light ( ) and the frequency of an electron

tunneling through the potential barrier ( t) are the preferred parameters for formulation.

Further, I is the ionization potential for the target electron energy level, m is the mass of

the electron, e is the charge of an electron, and E is the amplitude of the electric field

associated with the laser. The more common and convenient formula for this relation is

e

mI

t

2

.

1-7

p

p

U

I

2

.

1-8

11

Thus, the Keldysh parameter serves as a useful guide in determining the ionization

mechanisms most likely to be relevant within a given experiment and offers a simple and

concise manner of determining the significance of a laser’s electric field on those

ionization processes.

1.2.4 Predicting Ionization Rates

There are several contemporary theories which seek to characterize and predict

strong-field ionization behavior. The difficulty of predicting ionization rates is based

primarily upon the complexity of the target system. Theory developed by Ammosov,

Delone, and Krainov (ADK) [16] successfully models the ionization rates of the

hydrogen atom and noble gas species. Like many tunnel ionization theories, ADK is

based on the single-active electron (SAE) concept in which only the most weakly bound

electron is considered to be interacting with the incident electric field while all other

electrons in the system act as frozen spectators. This model has also been extended to

small molecules with some success in the form of molecular-ADK (MO-ADK) [17].

However, ADK and similar SAE-based theoretical treatments (such as those purported by

Perelomov-Popov-Terentev (PPT theory) and Keldysh-Faisal-Reiss (KFR theory) fail to

accurately model complex systems in which multi-electron effects are significant.

Further, the tunneling rates of these theories are based on the assumption that the

adiabatic approximation is valid, which limits the applicability of the models in many

systems, especially larger species and/or those containing numerous delocalized

electrons.

For example, ADK overestimates the ionization rate of transition metal atoms [8]

due to the presence of multiple weakly-bound valence electrons characteristic of open-

shell atoms. As these polarizable valence electrons are shifted towards the ionization

barrier by the external field, they create a significant repulsion towards the active electron

and thus increase the potential barrier for tunneling, suppressing ionization. Similar work

was also performed on small metal clusters [18] and the failure of SAE-based theories

12

was also reported. Clearly, as the molecular size and complexity increase, the

significance of multielectron effects in strong laser fields increases and the validity of the

quasi-static approximation is limited. Further, SAE theories often cannot be rationalized

at lower field intensities. There is significant work being performed in attempts to

accurately model the ionization behaviors for complex systems [19,20], but no clearly

defined theory has yet been reported. One of the most recently advanced theories is

referred to as the single-active electron time-dependent Schroedinger equation (SAE-

TDSE) theory [21] which has been shown to behave well in studies on molecular

hydrogen.

1.3 Enhanced Ionization Mechanisms

Unlike atoms, clustered and molecular systems can undergo enhanced ionization

beyond that which an external field could accomplish alone. This is due to the proximity

of multiple nuclei to one another within the polyatomic systems, the internal electric field

which results from the ionization of those nuclei, and the superposition of this internal

field with the external one from the laser. Specifically, the small internuclear distances

typical in a cluster allow for significant interactions between positively ionized nuclei and

their neighboring electrons. This internal field can combine with the potential well

deformation enticed by a strong external field to further ionize electrons into the

continuum. In addition, the characteristically high density of a cluster provides a

similarly high density of electrons which can provide opportunity for increased energy

absorption as the electrons interact with the laser field.

The applicability of each of the models and mechanisms described below is

dependent both on the nature of the cluster itself as well as the characteristics of the

incident laser field responsible for ionization. Thus, summaries of each concept are

delineated below while discussion of the intricacies and applicability of each of the

models germane to the studies contained in this thesis may be found in subsequent

chapters.

13

1.3.1 Ionization Ignition Mechanism (IIM)

The ionization ignition model (IIM) was first proposed by Rose-Petruck et al. in

1994 [22] and has found relevance in highly ionized systems of all sizes and

compositions. In their original calculations, Rose-Petruck and coworkers found that

following the single ionization of each atom within a 25 nuclei cluster, rapid multiple

ionization events took place at an unanticipated rate and Ne+8

ions were created within

1-3: Schematic depicting the effects of neighboring ions within a diatomic system which may lead to the

ionization ignition mechanism. Higher charges result in larger Coulomb attraction between an ion and

neighboring electron which reduces the energy required for removal of that electron. This behavior is

represented by the lowering of the potential barrier in the direction of the neighboring ion.

14

several femtoseconds. In this mechanism, the initial ionization events take place due to

field ionization at the leading edge of the laser’s electric field, which therefore must be of

sufficient intensity to promote those primary events. As the laser pulse continues to

increase in field strength as it propagates across the cluster, a second, internal potential

landscape is formed based on the attractive force exerted by each positively charged

atomic center on the surrounding electrons of the neighboring ionic cores.

This attractive potential draws the valence electron density away from the parent

nucleus, thus deforming the potential barrier and reducing the effective ionization

potential for emission of the electrons. As more electrons are removed, the charge state

of each nucleus becomes more positive and further lowers the barrier of the newly

exposed electrons on neighboring nuclei. In this manner, the external electric field is

capable of ionizing tightly bound electrons at significantly lower field strengths than

predicted based purely on atomic ionization potential values and thus the maximum

charge states attainable for the atomic species populating the cluster are increased beyond

that which would be accessible by the external field alone. A graphical depiction of this

behavior is illustrated in Figure 1-3.

By its nature, the IIM is most significant in systems in which the interatomic

distances between nuclei are as small as possible for the longest time possible, as the

effective barrier reduction diminishes with Coulomb’s law, and thus quadratically as

distance between nuclei is increased. Thus, IIM has a much more significant role in

experiments which employ an ultrashort pulse (<100fs) wherein maximum ionization

may occur with a minimum of cluster expansion. Short ionization times may further

enhance the influence of IIM by favoring outer ionization, which would remove ionized

electrons completely from the cluster and prevent the possibility of shielding by inner

ionized electrons. This mechanism is often referred to as cluster vertical ionization (CVI)

and denotes the outer ionization of a cluster without any significant changes in the

structure or internuclear distances associated with the neutral clusters. CVI most often

occurs in smaller clusters as they can possess both optical transparency to the external

field (allowing for all nuclei within the cluster to experience the same external field) and

dimensions small enough to inhibit electron retention (inner ionization). A useful

15

analysis of the direct influences of laser pulse width, frequency, shape, and intensity on

CVI have been performed by Last and Jortner [23].

1.3.2 Charge Resonance Enhanced Ionization (CREI)

First purported by Bandrauk and Zuo [24], the charge resonance enhanced

ionization (CREI) mechanism asserts that charge resonant states can become strongly

coupled to an intense electric field and result in the enhanced ionization of a cluster or

molecule in a nonlinear manner. Specifically, this method was developed by using

quantum mechanical formulations to describe the tunneling frequency of electrons

travelling between charged bodies when an external potential is applied to the system.

The model describes the motion of electrons between the ion cores initially created by the

external electric field and influenced by the internal electric field which develops via the

same phenomena as those involved in ionization ignition. This model is also referred to

as ENhanced IOnization (ENIO or simply EI).

According to the original formulation of the CREI model for the H2 system, as the

molecule stretches and the separation between the ionic nuclei increases beyond its

lowest energy interatomic distances, there will be a critical separation (Rc) at which the

ionization rate will be significantly enhanced. This approach relied on the importance of

the internuclear distance with respect to a balance between inner (the situation in which

an electron is removed from its parent nuclei but remains under the influence of the

system as a whole) and outer (wherein an electron is completely removed from the target

cluster) ionization rates. A simple graphical description of this concept is presented in

Figure 1-4.

Briefly, consider a diatomic system oriented parallel to the direction of the laser’s

electric field. At a small internuclear distance (a), the internal barrier between the two

nuclei is suppressed and electrons may cross freely between the potential wells. As the

distance increases, this internal barrier will also increase, while the external barrier to

outer ionization is suppressed to allow for higher tunneling rates. At Rc, a situation arises

16

wherein electrons may freely cross over the internal barrier and/or tunnel through a

significantly more narrow barrier and thus become ionized directly into the continuum

(b). The internal ionization barrier is further suppressed by the attractive Coulomb

potential exerted by the adjacent nuclei and is key to the enhancement of the ionization

dynamics. Finally, as the internuclear distance grows beyond Rc, the internal barrier rises

above the energy provided by the external field and the enhanced ionization process

ceases (c). It is important to note that this ionization enhancement, while it is the result

of cooperative effects, has no basis in the collective, coherent motion of multiple

electrons. Ionization enhancement resulting from those phenomena will be discussed in

the next subsection.

This model was further developed by Jortner et al. in 1998 [25] wherein the

model underwent a more classical treatment. Specifically, cluster structure was allowed

to change over time as the transient behavior of the laser pulse was evolving. This

dynamic internuclear distance between ion cores results in an inner potential barrier that

rises as time progresses. Specifically, as the positive cores push away from one another,

they are also shifted further from the neighboring valence electrons and thus they exert

less attractive force on them. This results in a higher ionization energy required to

remove a bound electron from its parent atom. Further, this behavior can lead to an

electron being trapped on one side of the bi-modal potential well or the other. As the

incident electric field reverses, the electron is given enough energy to cross the inner

potential barrier and thus leads to a net overall gain in energy from the electron’s

interaction with the field. This “jumping” process repeats until the electron energy is

sufficiently higher than the inner potential and the electron is released.

More recently, extensive strong-field ionization (SFI) theoretical calculations

were performed on small (16-30 atom) rare-gas clusters by Siedschlag and Rost [26]. In

these studies, they extended the enhanced ionization (ENIO) picture, which had been

previously only been applied to SFI in dimers and trimers, to larger clustered systems.

17

1-4: Schematic representation of the charge resonance enhanced ionization mechanism as it applies to a

diatomic system in the presence of a static electric field. As the distance between the two atomic species

grows (r’r’’’) the interaction between the potential wells changes accordingly. At small internuclear

distances, electrons may transfer between the two atomic cores but remain bound within the dimer (inner

ionization). At r’’, the interatomic distance is such that electrons can escape the potential well (via

tunneling or over the barrier ionization) on the left and then directly escape to vacuum (outer ionize).

Finally, at large interatomic distances (r’’’), electrons in the left well remained bound there, while ionization

may still proceed from the right potential well. Thus, ionization becomes enhanced at the intermediate

distance due to the simultaneous and cooperative suppression of the inner and outer potential barriers.

18

As a result of the broad scope of their study, Seidschlag and Rost were able to

observe the effects of a number of different variables on the enhancement of ionization

rates from rare gas clusters. For instance, they report a relative insensitivity to small

changes in the cluster size as well as to the applied laser frequency (which is in sharp

contrast to the collective electron motion mechanisms detailed in the following section).

However, they did observe an increase in maximum charge state for heavier constituent

atoms as well as with increasing laser intensity. Further, it was determined that larger

(again, 30 atoms vs. 16 atoms) clusters reach their maximum charge states at wider pulse

widths. For further details, please see Ref [26].

Two other recent studies are especially worthy of explicit mention in this section.

First, SFI calculations performed by Kamta and Bandrauk [27] on the heteronuclear

dimer He-H revealed that the orientation of molecular dipole with respect to the laser

polarization can have a dramatic influence on the ionization enhancement process.

Specifically, if the permanent dipole of the molecule is aligned antiparallel to the peak of

the external electric field, enhanced ionization proceeds much more favorably. While the

authors assert that this behavior should be universal for any nonsymmetric polar

molecule, it is important to note that the mechanism will only be manifested under the

influence of very short, few-cycle pulses. In the presence of longer laser pulses, the

effect will “wash out” over the course of the many-cycle averaged process.

Finally, in more recent theoretical work from Kamta and Bandrauk [28], it was

shown that the critical internuclear distance, Rc, only exists for electrons located directly

between two participating nuclei (i.e. in a sigma electron orbital). The calculations

demonstrated that off-axis electrons, such as those residing in a p-orbital, experience a

monotonic (albeit still enhanced) increase in ionization as internuclear distance increases.

Unfortunately, these simulations could only be performed on small diatomic systems and

thus the full implications of this phenomenon have not yet been determined.

19

1.3.3 Coherent Electron Motion Mechanism (CEMM) or Nanoplasma Model

In larger systems, where increased populations of delocalized electrons are

present, collective electron effects are possible. As a simple example, consider a cluster

composed purely of metal ions. The Jellium model [29-31] is commonly invoked for

gaining a qualitative understanding of the basic electronic structure within a metallic

cluster. Simply put, the delocalized nature of the valence electrons responsible for the

metallic bonding forces which hold the cluster together can be treated as a broad

negatively-charged distribution (1-5b) intermixed with a homogenous positively charged

background attributed to the metal nuclei (1-5a). Upon external stimulation (1-5c), the

loosely bound electrons localized within the cluster can become displaced relative to the

center of the positively charged core (1-5d). The cationic metal nuclei exert a restorative

Coulombic attractive force on the electron cloud and pull the electron density back

toward the cluster. In this way, the electron density wave adopts a coherent oscillatory

motion which travels at a certain frequency, similar to a plasmon in a nanoparticle.

Further, the specific frequency of this oscillatory behavior will be dependent upon the

strength of that attraction, which is dependent upon the composition, size, shape, etc. of

the cluster itself.

If this plasmonic frequency becomes resonant with that of an external electric

field, the energy absorption cross-section for the system increases dramatically and

results in the deposition of large amount of energy, which translates into heating of the

electrons, and thus leads to enhanced ionization as the oscillating electrons transfer this

energy to the cluster. It was on this basis that the coherent electron motion model was

proposed by Rhodes and coworkers in 1993 [32]. Since then, the model has been

successfully applied to small (20-100 atoms) [33], medium (100-1000 atoms) [34] and

large (>1000 atoms) [35] clusters composed of a variety of different species, although

assumptions of spherical shape and homogenous density within the cluster are typical.

Throughout the literature, CEMM is often referred to as the nanoplasma model,

especially when applied to larger cluster systems, but the ionization dynamics remain the

same. This phenomenon can be further extrapolated to nanoparticle systems, as the

20

cluster plasmon has a direct correlation with the nanoparticle surface plasmon, its

associated Mie frequency, and the energy absorption dynamics implicit in those systems.

Regarding the CEM model, the basic steps involved in the ionization process are

threefold: 1) field ionization to create and enhance the inner ionized electron cloud, 2)

electron collisional heating within the cluster as the electron cloud oscillates in the

external electric field, and 3) cluster expansion leading up to complete cluster destruction.

1-5: Schematic to illustrate the nature of a Jellium-type cluster and the onset of a cluster plasmon. The

nuclei and valence electrons which comprise the cluster may be thought of as diffuse positively- (a) and

negatively-charged (b) clouds. The interaction between the delocalized electron density and the inner

metallic ion cores results is a dynamic one and collective and coherent oscillatory behavior can be induced

by an external electric field (c). The cartoon of the waveform is misleading as the size of the target cluster

should be sufficiently smaller than the laser pulse that the entire cluster experiences an identical influence

from the field. The cluster’s frequency is unique to the size, dimensions, composition, etc. of a particular

cluster. See text for more details.

21

In step 1, the external field irradiates the optically transparent (depending on

composition) cluster material and inner ionizes a significant population of electrons via

tunnel or barrier suppression ionization. Throughout this process, the creation of ionic

cores will create an internal electric field which will serve to further suppress ionization

barriers, as in the two previously described models. As these electrons coherently

oscillate in the electric field, they will become collisionally excited via inverse

bremsstrahlung (IB) processes (step 2). IB excitation refers to the process of energy

absorption which occurs as an external electric field drives an electron in the field of a

nucleus. As the electrons within the cluster are heated, the cluster begins to expand via

hydrodynamic pressure. While the cluster expands, the respective plasmon frequency

gradually lowers in rate. Upon sufficient expansion, the cluster plasmon frequency can

come into resonance with the frequency of the external field, resulting in an immense

increase in the energy absorbed by the cluster and enhancing the ionization rate

significantly. This process continues until the cluster is no longer cohesively held

together.

The previous sections represent a concise overview of several important concepts

regarding the interactions of strong-fields with matter. The topic itself is quite broad and

far-reaching, and as such, even the lengthiest reviews must be limited in scope. Several

of the more useful and informative reviews have been consulted for this introduction and

as such, the reader is encouraged to investigate that literature and the wealth of references

found within each of them. Specifically, recent publications from Gibbon [36], Krainov

et al. [37], Posthumus [13], and especially Saalmann et al. [38], Bhardwaj et al. [39], and

Lezius et al. [40] will prove to be both enlightening and comprehensible.

22

1.4 References:

[1] Purnell, J., Snyder, E.M., Wei, S., Castleman Jr., A.W., Chem. Phys. Lett., 229 (4-5),

333-339 (1994).

[2] Thomas, J.M., Michael Faraday and the Royal Institution; Adam Hilger: Bristol,

1991.

[3] Castleman Jr., A.W., Bowen Jr., K.H., J. Phys. Chem., 100, 12911 (1996).

[4] Armentrout, P.B., Annu. Rev. Phys. Chem., 52, 423 (2001).

[5] Morse, M.D., Chem. Rev., 86, 1049 (1986).

[6] Lauher, J.W., JACS, 100, 5305 (1978).

[7] Alonso, J.A., Chem. Rev., 100, 637 (2000).

[8] Smits, M., de Lange, C.A., Stolow, A., Rayner, D.M., Phys. Rev. Lett., 93 (21),

213003 (2004).

[9] l’Huillier, A., Lompre, L.A., Mainfray, G., Manus, C., Phys. Rev. Lett., 48 (26), 1814-

1817 (1982).

[10] Keldysh, L.V., Soviet Physics JETP, 20, 1307 (1964).

[11] Kaiser, W., Garrett, C.G.B., Phys. Rev. Lett., 7 (6), 229 (1961).

[12] Voronov, G.S., Delone, G.A., Delone, N.B., Kudrevat, O.V., JETP Letters – USSR,

2 (8), 237 (1965).

[13] Posthumus, J.H., Reports on Progress in Physics, 67 (5), 623-665 (2004).

[14] Gets, A.V. and Krainov, V.P., J. Phys. B: At. Mol. Opt. Phys. 39, 1787-1795 (2006).

[16] Ammosov, M.V., Delone, N.B., Krainov, V.P., Sov. Phys. JETP, 64, 1191 (1986).

[17] Tong, X.M., Zhao, Z.X., Lin, C.D., Phys. Rev. A, 66, 033402 (2002).


203402 (2004).

[19] Brabec, T., Cote, M., Boulanger, P., Ramunno, L., Phys. Rev. Lett., 95, 073001

(2005).

[20] Brabec, T., Zhao, Z. X., J. Phys. B: At. Mol. Opt. Phys. 39, L345-L351 (2006).

[21] Awasthi, M., Vanne, Y.V., Saenz, A., Castro, A., Decleva, P., Phys. Rev. A, 77,

063403 (2008).

23

[22] Rose-Petruck, C., Schafer, K.J., Wilson, K.R., Barty, C.P.J., Phys. Rev. A, 55 (2),

1182-1190 (1997). NOTE: this reference is provided in lieu of the original paper, which

is currently inaccessible via most common sources.

[23] Last, I., Jortner, J., J. Chem. Phys., 121, 3030 (2004).

[24] Zuo, T., Bandrauk, A.D., Phys. Rev. A, 52 (4), R2511-R2514 (1995).

[25] Last, I., Jortner, J., Phys. Rev. A, 58, 3826 (1998).

[26] Siedschlag, C., and Rost, J.M., Phys. Rev. A., 67, 013404 (2003).

[27] Kamta, G.L., Bandrauk, A.D., Phys. Rev. Lett., 94, 203003 (2005).

[28] Kamta, G.L., Bandrauk, A.D., Phys. Rev. A, 75, 041401(R) (2007).

[29] de Heer, W.A., Rev. Mod. Phys., 65 (3), 611-676 (1993).

[30] Brack, M., Rev. Mod. Phys., 65 (3), 677-732 (1993).

[31] Ekardt, W., Phys. Rev. B, 29 (4), 1558-1564 (1984).

[32] McPherson, A., Luk, T.S., Thompson, B.D., Boyer, K., Rhodes, C.K., Appl. Phys. B.

57, 337 (1993).

[33] L. Koller, M. Schumacher, J. Kohn, S. Teuber, J. Tiggesbaumker, K. H. Meiwes-

Broer, Phys. Rev. Lett., 82 (19), 3783 (1999).

[34] Last, I., Jortner, J., Phys. Rev. A, 62 (1), 013201 (2000).

[35] Kumarappan, V., Krishnamurthy, M., Mathur, D., Phys. Rev. A, 67, 043204 (2003).

[36] Gibbon, Paul, Short Pulse Laser Interactions with Matter: An Introduction, Imperial

College Press, 2005.

[37] Krainov, V.P., Smirnov, B.M., Smirnov, M.B., Physics-Uspekhi, 50 (9), 907-931

(2007).

[38] Saalmann, U., Siedschlag, Ch., Rost, J.M., J. Phys. B: At. Mol. Opt. Phys., 39, R39-

R77 (2006).

[39] Bhardwaj, V.R., Rajeev, P.P., Corkum, P.B., Rayner, D.M., J. Phys. B: At. Mol. Opt.

Phys., 39, S397-S407 (2006).

[40] Lezius, M., Blanchet, V., Ivanov, M.U., Stolow, A., J. Chem. Phys., 117 (4), 1575-

1588 (2002)

.

Chapter 2

Experimental Setup: Apparati and Techniques

The experiments detailed within this dissertation are concerned with studies

investigating the interactions between matter and light. As such, the techniques used for

the creation and manipulation of this matter, in the form of clusters, as well as the

formation and utilization of the pulses of electromagnetic radiation used in studying these

clusters are discussed in this chapter. Further, the experimental apparatus used to detect

the species resulting from these light-matter interactions is described in limited detail. It

is the opinion of this author that the basic principles of the experimental apparatus have

been thoroughly covered elsewhere (for excellent background information, please see the

thesis of Wisniewski (Investigations of Molecular Clusters: Excited State

Photochemistry, Solvation Effects and High Energy Processes, 2002)) and abundant

resources are available. Thus, this chapter will mostly concentrate on the roles of each

apparatus within the overall system used in the performance of these experiments. Note,

however, that several of the experiments contained in later chapters required some

important modifications to the general approaches described herein and those details may

be found in the experimental sections of these subsequent chapters.

In each of these experiments, the clusters under investigation were created using a

laser vaporization (LaVa) source. Following the formation of the desired clusters, they

were exposed to femtosecond pulses of light obtained from a colliding-pulse, mode-

locked (CPM) dye laser and amplified in several stages to obtain sufficient intensity for

the chosen experiments. Detection of the resulting species was performed using a Wiley-

McLaren style mass spectrometer in conjunction with various ion beam-steering optics

and a micro-channel plate (MCP) detector. As with all gas-phase cluster research, these

experiments were conducted within a vacuum chamber. A schematic of the overall

source and detection scheme may be seen in Figure 2-1.

25

2.1 Cluster Source

Despite the fact that the experiments described within this work were performed

on many different clusters of varying sizes, compositions, bonding schemes, etc., they

were all created using a single source; a laser vaporization source based on the style

developed by the groups of de Heer [1] and Smalley [2] and further refined by the Penn

State Department of Physics Mechanical and Electrical Engineering department. This

type of source is widely used in the field of gas-phase cluster studies due to its simplicity,

robustness, and flexibility. A more detailed schematic of the source is provided in Figure

2-2.

2-1: A schematic representation of the cluster source and mass spectrometer. Following creation in the

laser vaporization source (a), the clusters traveled a short distance until they were irradiated with an

ultrashort pulse of light as they passed between the electrostatic grids which constitute the Wiley-McLaren

extraction region (b). Based on the electric field parameters of the extraction region, any cationic products

resulting from the laser ionization event were directed into the mass spectrometer, wherein they

encountered a beam-steering deflector plate (c) and an Einzel lens (d) prior to being detected at the

microchannel plate (MCP) detector (e) in the short field-free region experiments. For the long field-free

region experiments, the cationic products bypassed the detector located at (e) and traveled to the reflectron

assembly at (f) where they were turned back towards the secondary MCP detector at (g).

26

Within the source, a metal rod composed of the target material, typically a Group

III, IV, or V transition metal for these experiments, was ablated by an external laser. The

99% pure transition metal rods were ablated with 5-20 mJ of focused 532nm light

delivered from a Quanta Ray DCR-1 Nd:YAG laser operating at a 10Hz repetition rate.

The metal rods were constantly rotated and translated using a threaded rod assembly in

conjunction with a stepper motor to continuously expose a fresh region of the target rod

to the impinging laser to provide consistency in cluster composition, size, and production

2-2: Detailed schematic of the laser vaporization source used in these experiments. Briefly,

reactant/clustering gases were introduced via the inlet at (a) whereupon pulses of the gas were created using the solenoid pulsed-nozzle (b). At a certain time during each gas pulse, the second harmonic (532nm) of an

Nd:YAG laser was directed into the source (c) where it ablated a target metal rod (d) which was

simultaneously being rotated and translated to ensure a “clean” spot on the rod for each subsequent ablation

event. The position of this rod was maintained via a spring-loaded ball bearing guide (e) with the intent of

minimizing changes in interior source dimensions in case of rod imbalance. Following creation of the

metal-gas plasma, the ionized materials were directed into the waiting room (f) prior to escaping the source

via the expansion nozzle (g) and entering into the ionization region of the mass spectrometer.

27

intensity. It is important to note that the energy of the focused laser pulses was such that

the ablation of the target metal results in the creation of a plasma located directly above

the surface of the substrate. This plasma contained highly energetic ionic and neutral

atoms as well as free electrons and was vital in the creation of the homo- and

heterogeneous species studied in this work.

Concurrently, a short pulse of gas was introduced into the laser vaporization

source in a manner in which it passed directly over the metal plasma. The gas packets

were provided by a solenoid-driven pulsed nozzle (General Valve®, Series 9) which was

controlled by a pulsed-valve driver built by the Penn State Electronics Shop. The

composition of this gas varied based on the desired species. For the experiments

presented in this thesis, pure methane (CH4) was used for creating metal-carbide clusters,

oxygen (O2) seeded in helium was used for making metal-oxide clusters, and pure helium

was used in the formation of homonuclear metal clusters. Further details regarding these

compositions may be found in the subsequent chapters.

Typical pulses for the gaseous species were approximately 500us in duration and

the laser ablation event was timed so that the plasma was created very near the middle of

the gas pulse (see Figure 2-1). It was determined that this timing provided the highest

density of reactant gas over the laser-induced plasma and thus yielded the maximum

cluster intensity.

As the gaseous species flow through the plasma, they undergo decomposition and

ionization, adding to the plasma and collisionally moving the entire ionic cloud away

from the ablation site and towards the next stage of the source; the waiting room. Within

this waiting room, interatomic collisions allow for the reactant gases to interact with the

transition metal atoms while further collisions with helium atoms (when present) serve to

remove energy from the ionic cloud and cool the clustering materials. Upon reaching the

threshold between the waiting room and the expansion nozzle, a supersonic expansion

occurs due to the cluster materials leaving the relatively high pressures found within the

waiting room and entering the lower pressure environment within the chamber. This

expansion serves to further cool the clustered materials as their internal energies are

translated into kinetic energy. Several variations on the dimensions of the waiting room

28

and expansion nozzle were implemented and details of these modifications may be found

in the subsequent chapters.

Upon exiting the LaVa source, clusters were observed which possessed near

thermal energies and which have also been found to be internally cool [3]. This cloud of

clusters then encountered a skimmer nozzle with a 5mm orifice positioned 30cm from the

laser-cluster interaction region. This skimmer effectively eliminated any part of the

cloud which was not traversing relatively collinearly in the desired direction and resulted

in a well-defined cluster beam containing anionic, cationic, and neutral species.

2.2 Femtosecond Laser Facility

To perform strong-field ionization experiments, an ultrashort pulse of light

(<1000fs) possessing a large intensity (>1014

W/cm2) at its focal point was required. To

obtain these ultrashort pulses, a colliding pulse, passively mode-locked dye laser was

used while a single Bowtie amplifier and a series of three Bethune cell amplifiers were

utilized in achieving the energy density necessary to reach the desired laser intensities. In

this subsection, some vital details regarding the operation of the laser system are provided

and have primarily been adapted from the original user’s manual which was provided

with the laser kit. Additionally, operational details have been added based on this

author’s experience in working with the laser system.

2.2.1 Colliding Pulse Mode-locked (CPM) Dye Laser

Femtosecond pulses of light centered at 624nm and possessing an average of

200pJ of energy were created using a colliding pulse, mode-locked (CPM) dye laser

(CPM-1 from Clark Instrumentation). The laser used in these experiments was actually a

closely-related variant of the laser which provided the world with its first sub-picosecond

laser pulses in 1981 [4]. This particular CPM laser cavity (Figure 2-3) provided

29

ultrashort pulses on the order of 100 femtoseconds. The cavity consisted of a series of

optics in addition to two liquid sheets of organic material, one containing a saturable

absorber and the other a gain medium. The gain medium was composed of

sulfurhodamine 590 dissolved in ethylene glycol which was pumped by a continuous

wave laser (532nm, 4.75W all lines power). The gain medium emitted light in a

broadband spectrum, providing the wide range of frequencies required to create the

femtosecond pulses. The broadband nature of the pulse is necessitated by the Fourier

limit and the gain medium must therefore emit many wavelengths in order to be able to

amplify the femtosecond pulses. The saturable absorber used was 3,3’-diethyloxadi-

carbocyanine iodide (DODCI) and provided the pulsed nature of the pulse train while

acting to passively mode-lock the system due to its nonlinear transmissivity with respect

to the intensity of light. These two dyes were manipulated into thin sheets of liquid for

several reasons, namely to prevent saturation, reduce the potential for heating within the

materials, and to minimize lensing and reflections that would result from using a cuvette.

A set of 4 matched prisms provided the positive chirp necessary to compensate for the

self phase modulation and group velocity dispersion that the pulses obtain when passing

through the two dyes.

2-3: Schematic overview of the CPM dye laser and subsequent amplification apparati. Note the

compression gratings which, when present, recompressed the beam to yield pulses of ~100fs in width.

Without the gratings, 350fs pulses were attained. The recommended power distributions for the Nd:YAG

amplification system have been provided. Prior to entering the TOF-MS within the vacuum chamber, the

femtosecond pulse beam was focused down to intensities above 1014W/cm2 via a 50cm focal lens.

30

Typically, the intensity of the pulse train leaving the CPM cavity is somewhat

difficult to maintain at a constant level. Assuming that the cavity is well-aligned, the

most likely sources of instability are 1) the flowrate of the gain dye circulation jet, 2) the

concentration of the gain and/or saturable absorber dyes, 3) the cleanliness of the 4

prisms in the cavity, 4) the relative amounts of glass traversed through each prism, and 5)

the position of the saturable absorber jet with respect to the pulse train. Regarding the

flowrate of the gain dye circulator, it was found that a pressure of 20-22 psi in the

circulator resulted in the most stable and highest intensity pulse train. Often, given the

humidity of the laboratory, the laser dyes may also absorb water from the air, diluting the

dye concentration and changing the viscosity of the circulating medium. Care should be

taken to seal the circulation units as well as possible. Unless the prisms are cleaned daily

(using the recommended HPLC-grade methanol-soaked optical wipe technique) they can

become dirty and result in lower and/or inconsistent intensity. The relative amounts of

glass provided by each prism was also found to occasionally affect the laser intensity and

stability. Once enough glass has been removed from the cavity, one may benefit from

translating pairs of prisms in and out, using additional glass from one to compensate for

the removal of glass from another to maintain the ideal amount of glass while optimizing

the specific path of the laser beam. The final common source of instability and intensity

loss is actually the most frequent culprit; the relative location of the saturable absorber jet

with respect to the pulse train. Once mode-lock has been established, minute changes in

the plane perpendicular to laser propagation can result in significant effects regarding

laser intensity and stability.

2.2.2 Bowtie Amplifier

In order to obtain the energies required for the experiments described herein, the

200pJ pulses were amplified in four successive stages, the first of which contained a 6-

pass Bowtie amplifier and the last three composed of Bethune cell amplifiers. The

Bowtie amplifier consisted of a circulating dye cell containing the gain medium,

31

sulforhodamine 640 dissolved in a 50:50 mixture of methanol and water, a pump steering

mirror, and multiple highly reflective mirrors to allow for the multi-pass alignment of the

femtosecond pulse train. The mirrors were oriented in such a way that the femtosecond

pulses passed through the gain medium 6 times before finally leaving the cavity. The

gain medium was pumped by a portion of the 532nm second harmonic of another

nanosecond Nd:YAG laser (GCR-1 by Coherent Lasers) operated at powers of 500mW

which passed through the gain medium twice, having been reflected back through the dye

via a mirror on the far side of the circulation cell.

This single-stage multi-pass design allowed for 6 individual amplification events

per pulse while reducing the overall footprint of the system and facilitating an easier

alignment procedure. Further, each subsequent pass through the gain medium occurred at

a slightly different angle to minimize the interference effects between overlapping pulses,

a problem which could reduce the quality of the final beam. The 6 passes of the

femtosecond pulse train must overlap in the gain medium, however, to ensure that each

pass receives the maximum amplification possible at the area where the gain is most

efficient, thus minimizing wasted pump energy. This particular Bow-tie amplifier also

contained another organic dye jet of malachite green dissolved in ethylene glycol which

facilitated the reduction of amplified spontaneous emission (ASE). The ASE was an

undesirable result of the multi-pass gain phenomenon and could steal pump energy away

from the femtosecond pulses, reducing the efficiency of the bow-tie amplifier. The

percentage of ASE in the overall pulse was determined by measuring the CPM power

after all amplification was completed, then taking the same measurement with the

femtosecond pulse train blocked (typically on the far side of the output coupler, where

the pulse train leaves the ring cavity of the CPM) and subtracting the two values. Less

than 10% contribution from ASE was desirable, with lower contributions being preferred.

With regard to experimental technique, it was determined that a pump energy of

800mW provided optimal amplification when the pump beam was focused in such a way

that its focal point exists between the dye cell and the return mirror after the pump beam

has been reflected off of the return mirror. Further, it has been seen that if the pump laser

beam has enough energy that it can ionize the air at its focal point (clearly evidenced by a

32

“tacking” sound and bright bluish-white flashes at the focal point) then either the pump

power is too high or the concentration of gain dye wasn’t high enough and, as such, a less

than optimum amount of pump energy was being absorbed and thus transferred to the

femtosecond pulses.

Upon exiting the bow-tie amplifier, the femtosecond pulses had passed through a

sufficient amount of glass that they had gained a net chirp leading to a stretching of the

pulse width from their initial 100fs width to approximately 350fs. In some of the

following experiments, this pulse stretching was desirable in providing an easily

accessible 350fs pulse (following subsequent amplification). However, most experiments

benefitted from the use of the shortest pulse possible, which in this case was around

100fs. Thus, a matched pair of parallel recompression gratings was positioned in the

laser path immediately following the bow-tie amplification. These gratings provided a

net negative GVD by reflecting the longer wavelength components of the femtosecond

pulse at a sharper angle and thus provide slightly different path lengths for the various

frequencies which constitute the overall femtosecond pulse.

2.2.3 Bethune Cell Amplification

The last three stages of amplification were nearly identical, as they all utilized

Bethune cell [5] prismatic dye circulators to amplify the femtosecond pulses. The

Bethune cells each consisted of a large prism with a cylinder longitudinally bored

through its center, through which a solution of sulfurhodamine 640 mixed in 50:50

methanol to water flowed via a circulation apparatus. As with the gain cell located in the

bowtie amplifier, the Bethune cells were pumped with a portion of 532nm light from the

second harmonic of the same Nd:YAG nanosecond laser which pumped the bowtie. By

positioning the flowing gain medium and femtosecond pulses collinearly through the

center of the prism, amplification proceeded in a uniform manner as the internal

reflections of the prism supplied pump energy to the gain medium from 4 different

directions simultaneously.

33

The only major variations between these three stages were the size of the bore

diameter and the amount of pumping power contributed to the amplification unit.

Specifically, the Bethune cells possessed increasing bore diameters of 2mm, 6mm, and

12mm successively. Each successively larger Bethune cell received an appropriately

larger amount of pump energy; 250mw, 1.1 W, and 1.9 W (see Figure 2-3). These

energy distributions were accomplished via a series of reflecting optics, each of which

was responsible for separating out a specific amount of light for the Bethune cell in its

path. The first optic was a simple glass slide, which optimally redirected 10% of the

main pump energy. The second beam steering mirror optimally reduced the beam energy

by 33% while the final mirror directed all remaining pump energy into the final, largest

Bethune cell. It is also important to note that upon initiation of the laser amplification

process, the system should be allowed to run for 5-10 minutes prior to use to allow for

thermal equilibrium to be attained for each of the optics in the beam path as well as to

allow the pumping Nd:YAG laser to reach a stable operating situation. Failure to allow

sufficient time for the laser system to equilibrate may result in significantly larger

contributions from the ASE in the system and thus a reduced femtosecond pulse intensity.

Assuming the aforementioned pulse recompression had been implemented, the

femtosecond pulses emerged from the final Bethune cell amplifier with approximately

30mW of total energy (~5-10mW of which was ASE) and a pulse width of 100fs.

Without pulse recompression, the pulses emerged with a width of approximately 350fs

and roughly the same amount of energy. Consistent amplification was best observed

using a power meter, and inconsistent amplification could typically be attributed to an

excessive concentration of gain dye in either the Bowtie or Bethune cell amplifiers or a

timing issue between the nanosecond delay box seeding of the amplification Nd:YAG

laser and the femtosecond pulse train.

34

2.3 Time-of-Flight Mass Spectrometer (TOF-MS)

A time-of-flight mass spectrometer (TOF-MS) was used to analyze both the

species created by the LaVa source as well as the products resulting from the strong-field

ionization experiments performed on these clusters. This particular TOF-MS consisted of

an acceleration and extraction region positioned normal to the direction of cluster beam

propagation and built in the style developed by Wiley and McLaren [6]. Further ion

optics consisting of a deflector plate and an Einzel lens assembly helped to steer the beam

into the field free region wherein clusters were separated in time based on their differing

mass-to-charge ratios until they impacted the detector, a chevron stack of two

microchannel plates. On occasion, a reflectron was inserted into the path of the ion beam

to lengthen the field free region and increase resolution to aid in proper mass

identification.

2.3.1 Time-of-Flight Extraction Region

The first ion optics encountered by the cluster beam were the three stainless steel

plates that constituted the Wiley-McLaren style time-of-flight lenses (Figure 2-4). These

plates are oriented parallel to the direction of cluster beam propagation and as such

succeed in redirecting any charged species at an approximately normal angle to their

original path, given the appropriate applied voltages. The stainless steel plates are 2”x2”

and while the first plate in the series was solid, the extraction and acceleration plates each

contained a hole in their centers which was approximately 1/8” in diameter. Each hole

was overlaid with a fine nickel mesh to allow for the creation of a relatively uniform

electric field while still permitting product species to traverse through from one region to

the next. The relatively small dimensions of the center holes will be explained below.

The repeller plate and extraction plate were separated by 1.65cm while the extraction

plate and accelerator plate were 0.64cm apart.

35

During strong-field ionization studies, a static potential gradient was typically

applied across the grids. This served the dual purpose of deflecting any ionic cluster

species present in the cluster beam, thereby ensuring that neutral species were the only

clusters present upon ionization by the femtosecond laser pulses, as well as directing

these newly created ionic products into the mass analyzer region of the spectrometer

following ionization. Further, by defocusing the laser beam and thus lowering its

intensity, neutral cluster species could be singly ionized (likely via MPI) and the neutral

cluster distribution could be observed (see Figure 2-5 for a demonstration). On occasion,

this cluster identification technique was unsuccessful and thus a pulsed voltage was

applied to the grids to allow observation of the cationic cluster species for use as a

representation of the neutral species being studied via Coulomb explosion.

2-4: Schematic depiction of the extraction region (a), deflector plate (b), and Einzel lens (c) assemblies

including typical operational voltages. As the neutral cluster beam enters the region between the repeller

(at +4kV) and extractor (+2kV) plates, its constituents would be irradiated with an ultrashort, intense laser

pulse (not shown) and subsequently undergo SFI. The solid blue line represents a simplified view of the

assumed path taken by the resulting cations. Whereas their residual downward momentum might normally

force the majority of ions out of the range of detection in the mass spectrometer, the deflector plate, typical

held at a static voltage of 80-160V, compensates for the undesired motion and directs the majority of the products towards the detector. Simultaneously, the deflector plate serves to push any ionic products

resulting from SFI of background contaminants (dashed red line) off-axis and reduce their significance in

the mass spectra (extended path extrapolated for illustration purposes).

36

In addition to species identification, by manipulating the voltage gradient which

exists between the repeller plate and the extraction plate, information regarding the

overall kinetic energy release associated with the Coulomb explosion which followed SFI

experiments was obtained. Upon Coulomb explosion, fragments of the original clusters

were ejected in every direction with a kinetic energy directly related to the total Coulomb

repulsion felt by each individual atom with respect to the rest of the parent cluster. In the

linear TOF-MS used in the experiments it was only possible to detect a very small

portion of those fragments. Specifically, only those fragments ejected with a direction of

2-5: An ensemble of mass spectra obtained by varying the location of the laser’s focal point. In doing so,

the electric field strength which the target species were exposed to was also changed accordingly. The

furthest point on the z-axis represents the spectrum which contains ions created at the least focused (and

therefore least intense) part of the laser beam. There was little to no evidence of multiply-charged species

while most of the clusters become singly-ionized and arrive at the detector intact. As the focus was

incrementally tightened and the clusters were exposed to higher laser intensities (towards zero on the z-

axis), the larger clusters began to fragment and multiply-charged ions became evident in the mass

spectrum. The spectrum taken at the highest intensity for this experiment does not represent the maximum

available intensity, as this figure is provided for illustrative purposes alone. At the maximum field

intensity, the multiply charged ion signal dominated the spectrum and singly charged polyatomic species were rarely observed in any appreciable amount. The small throughput orifice in the extraction plate of the

TOF assembled aided in narrowing the observed species to those exposed to similar field intensities.

37

propagation directly paralleling the orientation of the mass spectrometer are observed.

Any fragments released with a vector which was more than a few degrees off-axis from

the path of TOF-MS traveled beyond the detection area of the spectrometer or collided

with a one of the surrounding ion optics (see Figure 2-6). This arrangement, despite the

fact that it greatly reduces the amount of observable signal resulting from a Coulomb

explosion event, allows the average KER of each cluster fragment to be observed

directly.

2.3.1.1 Kinetic Energy Release (KER) Measurements

Observation of the KER was possible due to the electric field located between the

repeller and extraction plates. In assuming that the only observable species resulting

2-6: Screenshot from a SIMION® simulation of a Coulomb explosion event within the confines of an ion

extraction apparatus similar to the one employed in these experiments. Although this is an idealized

situation, it is clear that despite the fact that ions may be ejected with vectors in any direction, only those

particles with a direction of propagation which is collinear (or very nearly so, at least) with the axis of the

mass spectrometer have the opportunity to be detected.

38

from the Coulomb explosion were those ejected directly towards or away from the

detector in the mass spectrometer, the process could be treated one-dimensionally.

Fragments ejected towards the detector gained kinetic energy equal to that with which

they were released from the cluster plus the energy gained from the distance they travel

with the static electric field provided by the TOF grids, resulting in a broad distribution of

energies. The fragments ejected away from the detector obtained the exact same amount

of kinetic energy and are turned back towards the detector in the presence of a strong

enough field. These ions become space focused and arrive in a relatively narrow

distribution. Using the peak analysis method, we measure the average time of flight

(TOF) for each peak distribution and input the Δt (in μs) into the equation

Where q is the charge of the ion, m is the mass of the ion in atomic mass units (amu), U1-

U2 is the voltage difference between the extractor and repeller plates in volts, while d is

the distance between the two plates in centimeters. The value 0.1204 is a constant

included to correct for the use of convenient units.

In several experiments, the relative KER was observed and utilized to discern

cluster expansion and/or to identify species within the ion distributions. In the former

application, cluster expansion was identified via an observed reduction in KER due to the

larger internuclear distances within the cluster leading to lower Coulomb repulsion

strength. In the latter use, an excellent example of the differentiation between

background species and clustered signal is demonstrated in Figure 2-7.

When obtaining background spectra for subtraction purposes, the LaVa source

was run in its typical manner with the exception that the vaporization laser was blocked

and thus the metal rod was not ablated. As such, the gas pulses of oxygen, methane,

and/or helium were still being produced and were accounted for within the background

spectrum. This was done with the intent of observing all species in the spectra which

were not products of the target clusters themselves, including the unclustered gaseous

species which were undoubtedly present in the cluster beam. Following SFI of the

. 2-1

39

background molecular oxygen dimer (from a transition metal oxide experiment), a

narrow peak splitting is observed for the O+ species in the “Background Spectrum”

shown by the dashed red line in Figure 2-7. The total spectrum (solid black line) and

subtracted spectrum (solid green line) are also provided in the figure. As shown, in the

“Total Spectrum” the KER splitting for the O+ species is rather difficult to discern due to

the additional contributions from the background O2 ionization. Following subtraction,

however, the splitting in the signal resulting primarily from the target clusters is clearly

observable and becomes sufficiently resolved to measure an accurate KER value. The

overall difference in average KER is also quite significant, as the energy released from

the O2 dimer was calculated (using Eqn. 2-1) to be < 1eV while the CE of the transition

metal oxide clusters yielded ~18eV of energy.

Figure 2-7 also contains several hydrocarbon ion peaks commonly observed in the

background signal which result from the SFI of hydrocarbon-based vacuum pump oil; a

contaminant within our vacuum chamber. As shown by the subtracted spectrum (solid

green line), the background hydrocarbon signal cannot be fully subtracted from the

overall spectrum, as the ion signal from these peaks increases in the presence of clusters.

This has been attributed to electron impact ionization resulting from the high density of

electron ejected via the SFI of the target clusters. This contamination and our techniques

to compensate for it are discussed in more detail in the following sections.

40

2.3.2 Deflector Plate

Upon exiting the extraction region, the cationic products immediately encountered

two additional ion steering elements. The first of these was a deflector plate to

compensate for the unavoidable downward momentum associated with the clusters due to

their expansion into the vacuum chamber upon leaving the LaVa source. The term

“deflector plate” refers to an assembly which consisted of two stainless steel plates

2-7: Demonstration of applications of kinetic energy release (KER) values. The solid black line

represents the overall spectrum obtained via SFI of transition metal oxide clusters and any background,

unclustered species in the path of the laser. The dashed red line shows several of the species commonly

observed in the background of our experiments while the solid green line is a subtracted spectrum which

results when the signal from the background is subtracted from the total spectrum. In this way, the KER of many species was obtained more easily and accurately. As noted, the hydrocarbon ion result from the SFI

of background vacuum pump oil and serve as an illuminating demonstration that the background oil

ionization increases in intensity during the ionization of the target cluster species. This has been attributed

to secondary electron impact ionization and makes it impossible to completely eliminate background

contaminant signal from the observed mass spectra.

41

oriented parallel to one another and collinearly with the direction of ion propagation in

the mass spectrometer (see Fig. 2-4). These plates were located approximately 1/2" away

from the acceleration grid, were separated from one another by 3/4", and positioned

slightly lower than the center of the hole in the accelerator plate. The top deflector plate

was held at local ground (zero potential) while the bottom plate possessed a static voltage

that was varied between 0V and +300V, although typical experiments required between

+80 and +160V.

This gentle voltage gradient served two vital purposes in these experiments. First,

whether the species under investigation were clusters or the fragments of clusters

resulting from a Coulomb explosion event, they possessed a certain amount of

translational momentum which was perpendicular to the axial direction of the mass

spectrometer (illustrated in Figure 2-4). Without being compensated for, this momentum

proved to result in the elimination of a significant amount of product signal as it carried

the cations out of alignment with the linear mass spectrometer. By applying a small

amount of corrective potential via the deflector plate, the flight path of the observed

species was corrected sufficiently to realign the particles with the preferred direction of

flight in the mass spectrometer without significantly altering the velocities imparted on

the particles in the extraction region.

The second important role of the deflector plate concerned the elimination of

background signal during Coulomb explosion studies. Due to the oil-based nature of the

vacuum pumping system used for these experiments, there existed a significant amount

of hydrocarbon-based pump oil present in the vacuum chambers. As these long

hydrocarbon chains were ionized by the incident laser pulses, they were also directed into

the mass spectrometer and subsequently detected (see, for e.g., Figure 2-7 and 2-8).

However, as these species were ambient within the chamber and possessed no coherent

path like that observed in the cluster beam, the oil molecules did not have a specific

innate kinetic energy for which compensation was required. Thus, as they traveled into

the deflector plate region, their direction of propagation was not corrected by the

electrostatic field, but rather the carbon species were forced off-axis and thus the

population which reached the detector was significantly reduced. This was quite

42

beneficial as elimination of these particles within the chamber proved extremely difficult

and their abundant presence in the mass spectra has been observed to mask the

populations of other species possessing similar mass-to-charge ratios.

2.3.3 Einzel Lens

Traditionally, a three-element Einzel lens is utilized to aid in space focusing ionic

products as they propagate through a mass spectrometer and thus increase the resolution

of the instrument. This particular Einzel lens was composed of three stainless steel

cylindrical coaxial electrodes of 1” in length, separated from one another by 0.1” and

positioned approximately 1/4" further downstream from the deflector plate assembly

within the path of the mass spectrometer (see Figure 2-4). The Einzel lens’ effectiveness

was limited in these experiments, as it was only employed in two specific scenarios due

to the fact that its use could significantly detract from the measurement of certain data.

43

Specifically, the Einzel lens was utilized when cluster signal (cationic as well as

ionized) was under observation. Further, the Einzel lens was used to recollimate the

portion of the Coulomb exploded signal that was travelling slightly off axis from the

direction of the mass spectrometer and which would not normally be detectable. This

technique was only used for species identification purposes in the long field-free region

experiments, where KER data was secondary. This was necessary because the

recollimation of the off-axis ions resulted in longer flight paths for those species and thus

particles possessing the same KE and m/z ratio experienced different times of flight.

2-8: Mass spectrum of the singly-ionized background contamination omnipresent in the vacuum chamber.

This spectrum was obtained by defocusing the femtosecond pulse train to allow for ionization without

Coulomb explosion. The inset spectrum contains several labels for the more intense peaks and demonstrates the abundance of species resulting from the fragmentation of large hydrocarbons. It should

be noted that this spectrum was obtained with the deflector plate held at a grounded potential to allow the

observation of the entire population.

44

This behavior would broaden the observed distributions and add inaccuracy in KER peak

analysis.

2.3.4 Detection: Microchannel Plate Detector

As noted in the overview above, two identical detectors were used in these

experiments and the only difference between the two was the position of each individual

unit. The detectors were both microchannel plate (MCP) detectors and were operated

without any additional post-acceleration or deflection modifications. The detectors

consisted of a matched pair of circular glass plates with circular electrodes positioned on

2-9: Experimental mass spectrum of the multiply charged ions which result from the laser-induced strong-

field ionization of background contamination. The hydrocarbon-based pump oil [(CH2)n where 20<n<40]

employed in our vacuum system is the most likely source of the majority of this contamination. Additional ions result from the SFI of water and nitrogen molecules. Unfortunately, simple background subtraction

techniques were typically insufficient for the elimination of this signal due to a noticeable increase in the

intensity of the ionized background species in the presence of the target cluster systems. This has been

attributed to electron- and ion-impact ionization of the background species resulting from collisions with

the highly energetic particles ejected during the Coulomb explosion of the parent clusters.

45

the top and bottom of the stack as well as an additional electrode located between the

plates to ensure electrical contact between them. These plates were oriented in a chevron

configuration, meaning that the angle of the channels located within the top plate was

positioned such that the channels were 180o opposite of those in the bottom plate. This

ensured maximum amplification in signal as the electron cascade proceeded. The total

electron signal was collected by a third plate, this one composed of stainless steel,

positioned several millimeters below the bottom of the rear glass plate.

The precise distribution of voltages to each element of the detector and the

amplification of final output signal was performed by a device designed and constructed

by the Penn State Department of Chemistry Electronics Shop. This unit was responsible

for redistributing the high voltage sent to it such that the front plate of the detector

remained grounded, the rear plate received voltage equal to 90% of the total sent to the

detector, while the rear plate received 100% of the initial high voltage. The high voltage

sent to the amplifier box was typically +2000V, as the thickness of these particular glass

plates restricted the total voltage across them to be less than 2000V in order to avoid

damaging the delicate material. This voltage distribution provided a strong positive

potential gradient to continually accelerate the electrons produced in the electron cascade

and aid in amplifying the signal. Further amplification was also performed within the

amplification box following reception of the output from the MCP detector. On

occasion, it was necessary to lower the initial voltage sent to the detector by as much as

500V to avoid oversaturating the detector in the presence of extremely large amounts of

ion signal.

2.4 Vacuum Systems

All of the experiments contained within this dissertation were performed within a

vacuum chamber. The main vacuum system consisted of two oil-based diffusion pumps,

two cold traps associated with the diffusion pumps, a turbomolecular pump, and the three

mechanical pumps used to provide a rough initial vacuum within the instrument as well

46

as back the main vacuum pumps when in operation. Typical baseline vacuum for the

overall chamber was maintained at approximately 3x10-8

torr in both chambers while the

pressures were elevated to 2x10-6

torr in the source chamber and 2x10-7

torr in the

detection chamber during operation. These values are just averages and conditions varied

during individual experiments; however, vacuum levels within the detection chamber

were rigorously maintained at pressures lower than 1x10-6

torr to avoid damaging the

MCP detector assemblies due to potential arcing between the interior elements of the

detectors. Thermocouple gauges were used to monitor vacuum within the chamber down

to pressures of 1.0x10-2

while ionization gauges were utilized beyond that limit.

The operating pressure within the source chamber of 2x10-6

torr roughly

corresponds to a number density of 3.5x1010

particles/cm3 and a mean free path of

5x103cm [7]. As noted previously, these conditions led to an observable presence of

background material within our experiments and two main sources of this contamination

have been discerned. Upon introducing the focused intense femtosecond laser into the

chamber in the absence of clusters, a well-resolved background spectrum can be

obtained, an example of which is shown in Figure 2-8. The most significant species

present upon ionization were the carbon monomer, its atomic higher charge states, an

array of singly ionized hydrocarbons, as well as water and species corresponding to its

incomplete fragmentation. It should be noted that Figure 2-8 represents the observable

background contamination under typical operating conditions. As discussed above, the

majority of the background was eliminated as a result of the proper use of the deflection

plate assembly to alter the path of the background species off-axis with respect to the

mass spectrometer.

Clearly, the two main sources of chamber contamination were water and

hydrocarbons of some unknown composition. Even at the lowest vacuum levels

obtainable in the current system, water was still present and thus was simply an

unavoidable contaminant. The most likely source of the hydrocarbon contamination was

the vacuum pump oil itself. Further, the oil used in the mechanical pumps which

provided backing vacuum for the diffusion pumps was the most likely culprit. The

diffusion pump oil, Santovac-5® (pentaphenyl ether, which is 5 benzene rings joined by 4

47

oxygen atoms between them, MW = 448 amu) has a vapor pressure of 5x10-10

at 20oC

and there were cooling baffles in place which prevented this oil from leaving the pump

and entering the vacuum chamber itself. While these cooling baffles should also have

inhibited the flow of the mechanical pump oil; however this oil has a vapor pressure of

~8.5x10-4

at 20oC and the likelihood of this species escaping the cold trap was much

higher compared to the diffusion pump oil. Following these findings, the previous

mechanical pump oil (VWR-19) was replaced with TKO 10 Ultra Mechanical Pump Oil,

which possessed a vapor pressure of 1x10-8

torr at 20oC, and foreline taps were installed

between the mechanical pumps and their associated diffusion pumps. Nevertheless, the

problem has persisted despite our courageous efforts to eliminate it.

48

2.5 References:

[1] Milani, P., de Heer, W.A., Rev. Sci. Instrum. 61, 3696 (1990).

[2] Maruyama, S., Anderson, L.R., Smalley, R.E., Rev. Sci. Instrum. 61, 3696 (1990).

[3] Hales, D.A., Armentrout, P.B., J. Cluster. Sci., 127, 1 (1990).

[4] Fork, R.L., Green, B.I., Shank, C.V., Appl. Phys. Lett. 38, 671 (1981).

[5] Bethune, D.S., Appl. Opt. 20, 1897 (1981).

[6] Wiley, W.C., McLaren, I.H., Rev. Sci. Instrum. 26, 1150 (1956).

[7] Building Scientific Apparatus, J. H. Moore, C. C. Davis, M. A. Coplan, Perseus

Books, Cambridge, Mass, 2003.

Chapter 3

Strong Field Ionization Studies of Transition Metal Oxide Clusters

As noted in Chapter 1, the overall premise of this thesis is the elucidation of the

strong-field ionization processes as they apply to small clusters. The studies delineated in

this chapter represent an exploration into the extreme ionization behaviors of covalently

bound clusters upon exposure to strong-field radiation. Specifically, we concentrate our

experiments on small (<50 atoms) clusters composed of early group IV, V, and VI

transition metals and their oxides when irradiated with ultrashort pulses of 624nm light at

intensities of > 1x1014

W/cm2. We found no conclusive evidence to indicate that

coherent electron motion plays a significant role in our observed multiple ionization

events. Further, we have obtained evidence that our clusters undergo enhanced ionization

most likely via the ionization ignition mechanism with possible contributions from the

so-called CREI process (please see Table 1-1 for mechanism summaries). Further, we

observe a logical progression of maximum charge states created within our clusters with

respect to their corresponding ionization energies. Specifically, the ionization of the

transition metal nuclei proceeds to a significantly greater extent than that seen for the

oxygen atoms due to the reduced ionization energies associated with the metallic species.

In the absence of complementary computational work, we provide several hypotheses,

based on our experimental findings, regarding the multiple ionization processes within

the targeted small clusters.

3.1 Introduction

The strong field enhanced ionization of clusters was first observed in the groups

of Castleman [1-3] and Rhodes [4]. The mechanisms leading to enhanced ionization in

50

the presence of a strong field and the subsequent Coulomb explosion dynamics have been

thoroughly investigated for both very small (2 atoms) [5] and extremely large (>500

atoms) clusters[6], both theoretically and experimentally. For most systems, the strong

field ionization behavior of small molecules and clusters is governed by a combination of

CREI [5] and the ionization ignition mechanism (IIM) [7] while large systems obtain

energy via electron-cluster interactions and have been described as nano-plasmas [8].

Despite the development of several models and theoretical treatments, experimental

investigations into the ionization behavior and explosion dynamics of small clusters (3-50

atoms) have received notably less attention.

Past studies of small clusters have been largely focused on those species

homogeneously composed of metal (Pb and Pt) or rare-gas (Ne, Ar, Kr, Xe) atoms. It has

been demonstrated that those clusters which display a metallic bonding character undergo

extensive ionization processes which rely on the delocalized electron nature of the cluster

[9]. The coherent electron motion of the inner ionized electrons may come into

resonance with the frequency of the incident strong field and lead to a significant increase

in the energy deposited into the cluster, resulting in extreme ionization of the constituent

atoms prior to Coulomb explosion. In rare-gas clusters [10], as well as small molecules

[11], the CREI mechanism reportedly dominates the multiple ionization behavior and has

been shown to be directly related to the interatomic distances associated with the cluster

or molecule. Specifically, at a certain interatomic distance (typically 2-3 times the

ground state interionic separation distance) the incident electric field interacts with the

target system in such a way that the barriers to inner ionization and outer ionization are

both suppressed sufficiently to lead to an increase in the ionization rate.

The transition metal oxide complexes studied in this work possess significantly

polar covalent bonding, in contrast to the rare-gas and metallic bonding schemes

discussed above. The strong electronegativity of the oxygen species creates a

heterogeneous electron distribution between an oxygen atom and a corresponding metal

nucleus. The effect of this electron-withdrawing character with respect to the

electronegativities of the various transition metals studied here could influence the effects

and contributions of ionization ignition as well as further ionization enhancement of the

51

metal cores based on CREI. Further, a significant majority of the covalently-bound

molecular systems which have been studied possess linear chains of hydrocarbon-based

species while the structure of our clusters is relatively more close-packed, and roughly

spherical, and composed of two types of nuclei with drastically different

electronegativities. Thus, these clusters represent a previously unexplored realm of

molecular/cluster interaction with strong fields.

This chapter, along with the following two chapters, is organized in the following

manner. First, a short summary of the pertinent experimental techniques and parameters

are provided. Secondly, in the Results section, m/z spectra are presented for the clusters

of each species as well as the highly charged ions resulting from strong-field ionization of

these clusters, along with brief descriptions of the important facets of each spectrum.

Next, analyses and discussion regarding the observed ions and ionization behaviors are

presented. Finally, an overall summary of results and conclusions are provided in the last

section.

3.2 Experimental

An extensive description of the experimental procedures used in these studies was

provided in Chapter 2, and thus only a brief summary will be given here in conjunction

with several important experimental parameters. Clusters were produced using a laser

vaporization source built in-house based on the design of Smalley [12]. Sample rods of

99% pure transition metals (Ti, V, Cr, Nb, and Ta) were ablated with the second

harmonic (532nm) of a Nd:YAG nanosecond laser (Quanta-Ray DCR®) operating at

300mW prior to being focused by a 30cm focal lens. A pulsed nozzle (General Valve®)

provided bursts of oxygen seeded in helium (~5% O2) which passed over the plasma

created by the ablation event. Following supersonic expansion into a vacuum chamber

(held at an operating pressure of ~5x10-5

torr) ionic and neutral clusters were formed and

subsequently skimmed into a 3mm molecular beam which propagated towards a Wiley-

McLaren style time-of-flight extraction region. The dual stage ion grid assembly was

52

typically maintained with static voltages of +4000V and +2000V, serving the dual

purposes of deflecting any ionic species present in the molecular beam and providing a

field of appropriate strength to direct the ionic fragments resulting from the Coulomb

explosion event toward the detector.

Following irradiation, the cationic products were accelerated into the time-of-

flight mass spectrometer which was operated in either short-field mode (field-free region

of ~1m) or hard reflectron mode. The reflectron was held at a static potential several

hundred volts greater than the potential on the extractor plate and provided a field-free

region totaling 2m. A beam steering assembly consisting of an Einzel lens and a

deflector plate was used to direct the ions into the field-free region. The products were

then detected via a microchannel-plate detector. Following the collision of the ions with

the detector, the resultant signal was amplified and directed into a digital oscilloscope for

averaging and data acquisition. Analysis was performed with a personal computer.

The size distribution of the target clusters was easily controlled by changing the

inner dimensions of the source’s expansion nozzle (see Section 4.2. for details). Small

clusters were selectively produced by utilizing a nozzle with a larger inner diameter of

3cm while larger clusters were created by using a nozzle of comparable length (3cm)

with an inner diameter of only 0.5mm. When possible, mass spectra of the neutral cluster

species present in our experiments were obtained by defocusing the femtosecond laser

beam to minimize the strong-field effects and allow the clusters to become singly ionized

with minimum fragmentation.

The Coulomb explosion events were triggered by a 100 fs pulse of 624nm light

generated via a colliding-pulse, mode-locked dye laser pumped with a continuous wave

VERDI® laser (Coherent) and amplified by a 6-pass Bowtie amplifier in series with three

Bethune cells. The amplification was provided by a second Nd:YAG nanosecond laser

(Spectra-Physics). Following amplification, the femtosecond pulse was directed into the

vacuum chamber and focused down to intensities approaching 1x1015

W/cm2 using a

40cm focusing lens. The entire experiment operated at a 10Hz frequency. Certain

experiments required the use of 350fs pulses of light which were created by simply

removing a pair of recompression prisms found in the amplification section of the

53

femtosecond laser assembly, allowing for consistent laser energies. Pulse widths are

measured via a single-shot autocorrelator and laser energies are obtained using a

Coherent Power Max® power meter.

3.3 Results

In the following section, the ion spectra obtained from these experiments will be

provided in conjunction with some analysis which focuses on highlighting various

important aspects of each spectrum which will be expounded upon in Section 3.4. In

several cases, vertical dashed lines have been supplied to help guide the eye to specific

peaks within the spectra. These lines were calculated using the overall spectrum

calibration and were intended to represent the exact m/z value at which a specific species

should appear.

3.3.1 Titanium Oxide Clusters

A representative mass spectrum of the titanium oxide clusters investigation is

provided in Figure 3-1. A mass spectrum of either the cationic or neutral clusters being

investigated was obtained for each experiment in conjunction with a mass spectrum of

the multiply charged ionic species for the purpose of demonstrating the range of clusters

being studied in this work. As shown in the figure, the spectrum was dominated by

clusters containing fewer than 15 total atoms with the maximum resolvable peak

representing Ti10O20. There was an approximate 1:2 ratio between metal and oxygen

atoms, a trend that is typical of these types of clusters formed via laser vaporization. It

should be noted that this spectrum depicts the cationic species created during these

experiments, as it was often found that observing the cationic species was more

straightforward than obtaining a spectrum containing the entire neutral cluster species,

which required ionization via the defocused CPM.

54

Figure 3-2 contains the mass spectrum obtained upon ionization of the clusters via

our intense 100 femtosecond laser pulse. The mass-to-charge ratio (x-axis) is plotted

logarithmically to highlight those species with the lowest m/z ratio, i.e. the most highly

ionized atoms. As noted in Chapter 2, despite our respectable vacuum conditions, use of

such strong radiation results in the ionization of every species near the focus of the beam,

including any background molecules. Of these, we typically attribute the majority of the

background H, C, N, and O ions to the strong-field ionization of water, hydrocarbons

from the vacuum pump oil, and molecular nitrogen leaking into the chamber from

atmosphere. Several of the most significant background species have also been labeled.

Unfortunately, this significant presence of background ionization results in an

obscuring of several of our target species in the mass spectrum due to unavoidable mass-

degeneracies. Specific examples found in the titanium oxide cluster experiments are the

3-1: Cationic mass spectrum of titanium oxide clusters.

55

overlap between O+ and Ti

+3 (15.9994 amu and 15.9667 amu, respectively), C

+ and Ti

+4

(12.011 amu and 12.975 amu), and C+2

with Ti+8

(6.0055 amu and 5.9875 amu).

Fortunately, the isotope distribution for the titanium atoms is sufficiently well-resolved to

allow differentiation between the background species and some of the lesser populated

isotopes of the metal species. Upon reaching higher charges states, however, this isotopic

splitting becomes less significant and proves less useful in species identification; i.e. the

mass-degenerate peaks C+2

and Ti+8

. Species identification is further complicated by the

fact that a simple background subtraction is insufficient for eliminating signal which

cannot be attributed to our target clusters because the background carbon, nitrogen,

oxygen, and hydrogen peaks which appear in our spectrum actually increase in intensity

in the presence of cluster ionization. This is likely due to electron impact ionization of

background species as a result of the highly energized electrons ejected from the target

clusters and thus an inescapable contamination without significantly improved vacuum

conditions. Hence, some species identification required a combination of spectrum

calibration, isotopic identification, and background subtraction. The results of this

analysis led to the m/z assignments and ion identifications depicted in Figure 3-2 for the

strong-field ionization of titanium oxide clusters.

56

The maximum charge state which was unambiguously observed for the titanium

ions was Ti+10

while the O+6

signal is also fairly distinct. The m/z peak associated with

the Ti+8

/C+2

shows a significant increase in intensity relative to the background spectrum,

which may or may not indicate the presence of the Ti+8

species. Likewise, the Ti+9

(m/z

= 5.32) signal was well overlapped by the O+3

(m/z = 5.333) present in both the

background and as a result of the cluster explosion. The presence of the Ti+10

(m/z =

4.79) is indicated by the small peak on the right side of the significantly more intense N+3

(m/z = 4.6689) peak. There is an unidentified peak at m/z ~ 4.166 which could possibly

be attributed to Ti+11

(m/z = 4.3545) but the m/z difference between these two is likely

sufficient to rule out such an assignment. Thus, we observe that the highest charged

3-2: Mass spectrum of the highly charged ionic species which result from the Coulomb explosion of

titanium oxide clusters. Note the maximum observed charge states for the target species are Ti+10 and O+6.

The isotope distribution for titanium is clearly seen for charge states +1 thru +5. Any areas in which mass

degeneracies between target species and background contributions are noted. See text for details.

57

metal ion resulting from the intense ionization and subsequent Coulomb explosion of

titanium oxide clusters is the Ti+10

charge state.

Further, we clearly resolve highly charged oxygen ions ranging from the O+

through the O+6

charge state. A background scan demonstrated a maximum charge state

of O+3

, indicating that the most highly charged oxygen ions are only produced via

multiple ionization of the target cluster species. This differentiation may be further

verified by comparing the KER of the oxygen signal resulting from the background gases

with that observed in the presence of clusters, as demonstrated in Figure 2-7 of Chapter 2.

It should be noted that the lack of KER peak splitting in this spectrum, and several of the

following spectra for other cluster species, is the result of the manipulation of the

voltages applied to the electrostatic ion elements to reduce splitting in conjunction with

the use of the longer field-free region to aid in attaining maximum peak separation for

facile species identification.

3.3.2 Vanadium Oxide Clusters

The second system under investigation contains the next more massive transition

metal in the row; vanadium. This species has only one dominant isotope for its metal

component and lacks a significant amount of mass degeneracy with either the background

signal or the cluster-born oxygen species. Again, the larger component of this

distribution tends to favor a MnO2n composition and the largest resolvable cluster

contains fewer than 40 total atoms. This distribution is depicted in Figure 3-3.

58

As noted above, the highly ionized distribution resulting from the strong-field

ionization of our clusters demonstrates clearly resolved ionic charge states ranging from

singly-charged V+ up to a small amount of V

+9 (Figure 3-4). Further, these trials

demonstrate little to no contribution from nitrogen based species. The cause for their

prevalence in some experiments and absence in others is currently unknown but can

likely be attributed to the vacuum conditions of the chamber and/or the presence of

nitrogen based contaminants in either the ablated metal or clustering gas used in the

source. The relative contribution from the V+9

species is quite small and is typically only

resolvable under ideal conditions in which the small shoulder can be resolved separately

from the larger C+2

signal. Peak splitting due to KER resulting from the CE of the

3-3: Typical cationic mass spectrum for vanadium oxide clusters.

59

background hydrocarbons was minimized via adjustments to the extraction field voltages

and use of the reflectron mass spectrometer in long field-free mode.

Similarly to the titanium oxide studies, we observe oxygen ions in a maximum

charge state of O+6

. Like the V+8

species, the O+5

and O+6

ions are difficult to create and

observe while typically requiring excellent ion focusing conditions and a large birth

potential. Despite their low intensity, the peaks correlating to these species arrive exactly

at the appropriate time-of-flight and thus we are confident in their presence. The

intensity of the peaks is significantly reduced by the inherent temporal spread of the

species in the field-free region as a result of the extremely large amounts of kinetic


vanadium oxide clusters. Note the maximum observed charge states for the target species are V+9 and O+6.

The spectrum has been truncated slightly to focus on the maximum observable charge states of the metal

species.

60

energy donated to these very light mass, highly charged ions following Coulomb

explosion. In addition, the population of these ions which are ejected with such energy

that they are unable to be turned by the potential gradient in the extraction region are not

detected.

3.3.3 Chromium Oxide Clusters

The chromium oxide cluster species is the final system involving a row IV

transition metal species investigated in these experiments and completes a representative

sampling of this row, providing an interesting series of experiments for comparison.

Figure 3-5 contains a representative cationic cluster distribution used in this set of

experiments. The typical MnO2n stoichiometry associated with the previous two systems

appears to become dominant at slightly heavier clusters while lighter species tend to be

less oxygenated. The largest resolvable clusters for this experiment continued to number

fewer than 40 atoms.

The isotopic distribution characteristic of chromium is clearly resolved in the Cr+2

and Cr+3

species yet disappears for any ions which have been more fully ionized (Figure

3-6). However, due to a lack of any significant mass degeneracy issues, this feature is

not necessary for species identification. In keeping with the relative trend observed

across this row, the chromium oxide clusters produce a maximum charge state of Cr+8

.

This ion is possesses a m/z of 6.4995 is not mass-degenerate with any common

background species. With a mass-to-charge ratio of 5.777, the Cr+9

species should appear

slightly to the left of the C+2

signal but its presence cannot be definitively resolved due to

the unavoidable width (resulting from a range of KER values) of the C+2

peak. It is

interesting to note, however, that there is a significant shoulder on the leftmost slope of

the C+2

signal which could potentially correlate to an underlying contribution from the

Cr+9

ion population. This likelihood will be examined in a later section.

61

Also consistent with the former two systems, we observe oxygen atoms ionized

up to the O+6

charge state resulting from the Coulomb explosion of chromium oxide

clusters. Again, the contribution of this species is very low in intensity, but the signal is

clearly present in appreciable amounts. Background signal from nitrogen-containing

species is insignificant beyond the N+2

charge state.

3-5: Typical cationic mass spectrum for chromium oxide clusters.

62

3.3.4 Niobium Oxide Clusters

For the niobium oxide cluster distribution (Figure 3-7) we present a spectrum

obtained via multiphoton ionization using the defocused CPM. The range is similar to

those shown before insofar as the size of the observed clusters does not exceed 40 atoms

(a cluster of 31 atoms is the largest seen here) and there is an approximate MnO2.5n

stoichiometry between niobium and oxygen. The overwhelmingly large contributions

from the mono-niobium oxide species is likely the result of cluster fragmentation


chromium oxide clusters. Note the maximum observed charge states for the target species are Cr+8 and O+6.

As discussed in the text, the Cr+9 ion may also be present, but masked due to a near mass degeneracy with

C+2.

63

resulting from over-excitation of the larger clusters. It is difficult to control the

multiphoton ionization events via this defocusing approach and thus, the relative

intensities of this spectrum may not prove wholly accurate with regard to the actual

neutral cluster distribution. Regardless, the technique yields a mass spectrum which

serves as an example of the species likely present in the neutral cluster beam.

The mass spectrum recorded following the strong-field ionization of these small

niobium oxide clusters is shown in Figure 3-8. Similarly to the zirconium oxide cluster

trials, we observe the removal of a maximum of 11 electrons from the transition metal

and a maximum of 6 electrons from the oxygen atoms. The only significant mass

degeneracy between the target species (and the background contamination) is manifested

3-7: Typical neutral mass spectrum for small niobium oxide clusters. This spectrum was obtained via the

defocused ultrafast ionization laser. The CPM pulse was typically defocused by ~3cm, resulting in

intensities of ~1x1012 W/cm2.

64

in the overlap between Nb+6

(m/z = 15.4844) and O+ (m/z = 15.9994) but the obvious

presence of more highly charged niobium ions is evidence for the existence of the Nb+6

species. Again, this spectrum has been plotted logarithmically along its x-axis to allow

for ease of species identification.

Another interesting facet of this spectrum is the presence of NbO+2

. The

production of multiply-charged polyatomic fragments results from incomplete charging

and/or Coulomb explosion and we observe a more significant presence of these fragments

with the heavier transition metal species. The larger size of the metal atoms creates a

more delocalized electron cloud which in turn allows the metal and oxygen atoms to

remain associated with one another despite the loss of multiple electrons. The dimers

may still fragment in the field free region, but clearly the species remain cohesively

bound throughout the ion extraction process.


niobium oxide clusters. Note the maximum observed charge states for the target species are Nb+11 and O+6.

65

3.3.5 Tantalum Oxide Clusters

Figure 3-9 contains a typical cluster mass spectrum for small tantalum oxide

clusters. The preferred stoichiometry appears to be MnOn for this distribution, similar to

several of the species described above. However, the overall number of atoms

constituting the resolvable species is significantly lower than that of the previously

discussed spectra, containing clusters with a maximum of 15 atoms. Heavier

distributions were also created and studied, and are discussed later. Regardless, as shown

in Figure 3-10, strong-field ionization of these clusters results in high ionization states.

Depicted in Figure 3-10, we observe clearly discernable transition metal ions up

to Ta+10

with the presence of Ta+11

highly probably due to the sharp shoulder evident on

3-9: Typical neutral mass spectrum for tantalum oxide clusters. Again, the CPM was defocused to obtain

an approximate intensity of 1012 W/cm2.

66

the high m/z side of the O+ peak. Unfortunately, there were significant contributions

from the background in this spectrum (and throughout this set of experiments) and the

next 3 levels of ionization for the tantalum ions are nearly perfectly mass degenerate with

commonly observed contaminants. Specifically, Ta+12

(m/z = 15.07899), Ta+13

(m/z =

13.91907), Ta+14

(m/z = 12.9249), and Ta+15

(m/z = 12.06319) could be overlapped by

CH3+ (m/z = 15.0347), CH2

+ (m/z = 14.0268), CH

+ (m/z = 13.0189), and C

+ (12.011).

Ta+16

has a mass-to-charge ratio of 11.309 is not mass degenerate with any typical

background contaminants; however, there is no evidence of signal at this value.

3-10: Mass spectrum of the highly charged ionic species which result from the strong field ionization

(I~1015W/cm2) of tantalum oxide clusters. Note the maximum observed charge states for the target species

are Ta+11 and O+6. Higher charge states of tantalum may be present but masked by the mass-degeneracies

with the background contaminants. See text for details.

67

We observe the ionization of oxygen to the +6 charge state for these studies. O+5

is clearly evident while the signal for O+6

manifests itself as a shoulder on the side of a

hump in the spectrum which results from the ringing in the baseline typical of

oversaturation of the microchannel plate detector (from the overwhelming H+ signal in

these experiments). Upon comparison with the background spectrum, the peak for the

O+6

ion is clearly present.

3.4 Analysis and Discussion

Based on our typical femtosecond laser parameters, we reach power densities of

approximately 1x1015

W/cm2 at the focal point of the beam. Using the equation

where I is the intensity of the laser at its focus (in W/cm2) and λ is the central wavelength

of the incident radiation (in micrometers) we can obtain the ponderomotive potential (in

eV) associated with the laser pulse. In its simplest sense, the ponderomotive potential

represents the average amount of energy an electron can gain as it oscillates in an electric

field. In this case, using the above intensity and a wavelength of 624nm, Up is

approximately 36.3eV. Clearly field ionization alone would be insufficient to strip more

than the first 3 electrons from any of the transition metal species studied in these

experiments (with the possible exception of the tantalum monomer, with a 33.1eV barrier

for the emission of its 4th

electron). Therefore, the clustered nature of our target systems

must be enhancing the ionization behavior we observe in our experiments. The following

discussions are provided to categorize and understand this ionization enhancement.

Due to the fact that many current theories regarding enhanced ionization

processes depend on strong-field effects, it is worthwhile to determine whether our

experiments fall within this regime. Upon reaching certain laser intensities,

photoexcitation behaviors lose their multiphoton character and tunnel ionization

processes can significantly contribute to the electron dynamics. The barrier at which this

Up= 9.33x10-14

I λ2 3-1

68

transition occurs is conventionally defined using the Keldysh, or adiabatic, parameter (γ).

This simple approximation is based on the ionization potential (IP) of the target species

and the ponderomotive energy of the incident electric field calculated above. In this

relationship, where

and if >1 then ionization is dominated by MPI while values of <1 indicate tunnel

ionization as a significant mechanism. Given the first IP of atomic niobium (6.5eV) this

equation yields a Keldysh parameter of ~0.3 while the first IP of atomic oxygen

(13.62eV) results in a value of ~0.43, both values clearly indicative of significant tunnel

ionization character.

An overview of the maximum observed charge states for all of the transition

metal oxide cluster systems described above may be found in Table 3-1. There are

several obvious trends which deserve further discussion. For the purpose of examining

these two particular trends, we shall restrict the discussion to two sets of experimental

data; those composed of transition metals in row IV of the periodic table (TixOy, VxOy,

and CrxOy) and those containing Group V transition metals (VxOy, NbxOy, and TaxOy).

The first trend in maximum charge states is manifested in the cluster species

containing row IV transition metals. As shown in Table 3-1, the maximum charge states

observed for the transition metal species steadily decrease with a corresponding increase

in atomic mass while the oxygen species for each cluster series result in identical charge

3-2

3-1: Table presenting the maximum observable charge states (MOCS) resulting from the SFI of each

transition metal oxide cluster series.

Ti V Cr Nb Ta

Metal +10 +9 +8 +11 +11

Oxygen +6 +6 +6 +6 +6

69

states of O+6

. Regarding the trend observed in the maximum charging of the transition

metal species, the reported atomic ionization energies lend some insight into this

behavior. Despite the clear presence of ionization enhancement mechanisms, several of

which manifest themselves by reducing the relative ionization potential for electrons

leaving their parent nuclei, the baseline ionization energies for the unperturbed atoms

serve as a reasonable (and convenient) template for comparing the relative amount of

energy which is donated to a particular species. Ignoring the specific perturbations

created by the ionization enhancement mechanisms, the original IE values still represent

the total amount of energy which must be donated to the electron to remove it, whether

that energy be donated via intracluster interactions or the external field.

The atomic IE values available from the literature [13] for each of the three Row

IV metal species are plotted sequentially in Figure 3-11 with the maximum observed

charge states observed in these experiments highlighted and several specific ionization

energies provided. Regarding the overall ionization energy trends displayed in Figure 3-

11, the first several ionization energies for each species are quite similar, as expected,

with the energies of the heaviest atom slightly higher than the lighter ones due to the

additional protons exerting stronger attraction to the electrons added into the same

electronic subshell. The large jump in ionization energy for each species (5th

for Ti, 6th

for V, and 7th for Cr) indicates the complete removal of all 3d electrons and the stripping

of the first 4s electron from the atom.

Initial inspection of the maximum observed charge states shows that the energy

required to ionize the 10th

electron from a bare titanium atom is approximately 216eV

while the energies required to create V+9

and Cr+8

are approximately 206eV and 185eV,

respectively. The appearance of each of these three species demonstrates that, regardless

of the transition metal component, the ionization dynamics within each cluster system

proceed to an extent which enables the creation of ions requiring more than 185eV of

energy, prior to the explosive fragmentation of the cluster itself. The clear absence of the

Ti+11

ion (or any higher charge states of the other species) is demonstrative of the fact that

the most energy which can be donated to clusters of this size, under our specific laser

conditions, is somewhat less than 265eV of energy, which is required for the creation of

70

that charge state. Using similar logic, we can assume that, in the absence of observable

V+10

ions, the ionization dynamics within the clusters do not allow the creation of ions

requiring 230.5eV of energy or more.

The relative mass degeneracy of the Cr+9

(5.77amu) and C+2

(6.0055amu) ions

(see Section 3.3.3 above) which results in the irresolution of the presence of the Cr+9

ion

is quite unfortunate, as its creation appears likely based on the reported ionization

energies shown in Figure 3-11. Approximately 209eV is required to remove the 9th

electron from a chromium atom, which is slightly less than that required for the observed

Ti+10

charge state. Assuming similar ionization and energy absorption processes between

the two species, the most likely reasons for the absence of Cr+9

are either the mass

degeneracy issue discussed above, or the relative intensity of the ionization laser. It has

been shown [10] that lower ionization laser intensities result in the production of lower

3-11: Graphical depiction of the reported sequential ionization energies for the Group IV metals and

oxygen. The energies which correspond to the maximum observed charge state for each metal are

highlighted and relevant energies are provided.

71

charge states for small rare gas clusters, and although the laser intensity was well

monitored and maintained for the majority of these experiments, it is possible that the

maximum laser intensity was simply not as high during these trials. Although, as it will

be discussed later in the chapter, upon reducing the ionization laser intensity

approximately an order of magnitude (via pulse width expansion), identical charge states

were observed for the SFI of niobium oxide clusters.

Based on these arguments, the production of O+6

ions and the absence of the O+7

species are unsurprising. The ionization energy required for O+6

is approximately 138eV

(see Figure 3-11) and is significantly less than the energy needed to create the maximum

metal charge states. Meanwhile, the IE for O+7

(the creation of which represents the

removal of a 1s electron) requires approximately 739.3eV of energy, well beyond the

limit of energy absorption expected for these studies. This data point was omitted from

Figure 3-11 to provide a clearer depiction of the lower energy values which are pertinent

to the transition metal atomic species.

Thus, it appears that the relative ionization energies of each transition metal

species in Row IV (and their counterpart oxygen atoms) can be directly related to the

maximum charge state observed for each species. This same principle can be applied to a

rationalization of the increase in maximum charge state observed as we compare species

from the same column on the periodic table; specifically the Group V transition metals.

There is a general trend in the periodic table in which as atomic number increases within

a family, ionization energy decreases accordingly. This is due to an increase in the total

number of energy levels and the accompanying increase in shielding for the valence

electrons by the increased number of inner electrons. This phenomenon results in a

down-shifting in the atomic energy levels. This trend, although fairly consistent across a

significant portion of the periodic table, does not always hold true for the transition

metals due to the large number of delocalized valence electrons characteristic of the d

shell. However, as shown in Figure 3-12, the trend in ionization energies for niobium

appears to abide by this guideline and the values are consistently lower than those

reported for vanadium atoms.

72

In fact, the energy required to remove the 10th

electron from niobium (which is

the highest charge state for which literature data was available) approaches 193eV, less

than the energy necessary to create the observed V+9

ion (~206eV). Due to the fact that

the 11th most tightly bound electron of niobium would be removed from the same 4p

energy orbital as the previous 5 electrons, the increase in IP should be approximately the

same as that from the 9th

to the 10th electron, ~21eV. The removal of the 11

th electron

from niobium would therefore require around 214eV, which means the appearance of the

Nb+11

ion agrees well with the previously discussed ion species from the Row IV series

and demonstrates that ions which require similar amounts of energy to create are also

produced in the presence of enhanced ionization phenomena. The appearance of O+6

in

the niobium oxide cluster experiments thus follows logically as well. Regarding the

creation of V+9

and Nb+11

under similar laser and clustering conditions, this behavior has

3-12: Graphical depiction of the ionization energies for the Group Vb metals studied in this work. The

energy necessary to create the Nb+11 ion is assumed based on the arguments provided in the text.

73

been observed in theoretical [10] as well as experimental [14] work performed on several

homonuclear (albeit different in composition from those observed here) cluster systems.

In these studies [10,14], it was shown that under identical clustering conditions,

irradiation conditions, and cluster structures, the strong field ionization of clusters

composed of less massive atoms results in the production of lower-charged ions.

The ionization energy data for the third species in Group Vb, tantalum, is

truncated (Figure 3-12). However, the energies which are reported (up to Ta+5

) are

consistently lower than those required to create similar charge states in vanadium as well

as niobium, likely indicating a continuation of this trend. However, as shown in Table 3-

1, there is no clear evidence of tantalum charge states beyond the +11 charge state,

identical to niobium. Higher charged states may be present, but due to mass degeneracies

with other species, they are not resolvable in our current experiments. Interestingly, if

the ionization process does terminate with the creation of Ta+11

, identical to the niobium

studies but more highly ionized than the Row IV member of Group Vb, it would not be

unprecedented. Meiwes-Broer and coworkers observed a maximum charge state of +10

for copper clusters, while Au+15

and Ag+15

were both created under identical experimental

conditions [14]. Each of these metals is also located within a single Group in the periodic

table.

As detailed in the above discussion, the highly charged ions resulting from the

strong-field irradiation of the target clusters cannot simply be originating from field

ionization, as the ponderomotive potential of the field is insufficient in magnitude.

Several enhanced ionization mechanisms have been observed both experimentally [9] and

theoretically [10] in systems containing similar numbers of atoms to those studied here.

Specifically, IIM and CREI have been shown to play significant roles in enhancing the

ionization rates of small molecules and clusters [5,7,11]. In somewhat larger clusters

(>50 atoms, typically) another mechanism begins to contribute to the ionization processes

and involves the coherent motion of inner ionized electrons within the cluster (CEMM).

It is worthwhile to note that electron recollision within a system has also been shown to

donate significant amounts of energy in various experiments [15]. However, the systems

described herein are too small to allow for any significant contributions from

74

electron/cluster recombination [16], as the mean free path of the electron is larger than

the collisional cross-section of clusters this size. Thus, effects from this particular

phenomenon will be ignored and the role of the IIM, CREI, and CEM ionization

mechanisms will be explored in more detail.

Based on the above arguments, it is reasonable to assume that any enhanced

ionization we observe in our experiments results from ionization ignition, charge-

resonance ionization, and possibly coherent electron motion. Studies by Kjeldsen et al.

found that for linearly polarized light incident on an H2 molecule, the ionization rate for

the electrons was highest when the molecule was oriented parallel to the plane of

polarization of the laser [17]. Given the multidimensionality of our systems, the

probability of this preferred bond orientation would be relatively higher. Further, the

ionization behavior of electrons affected by CREI has thus far been restricted primarily to

electrons participating in bonding between two nuclei. The effects of internuclear

distance with respect to heteronuclear, highly charged species such as those discussed

here have been largely neglected. Recently, however, research from the Bandrauk group

has shown that the characteristic “critical internuclear distance” or Rc for maximum

enhanced ionization applies only to bonding electrons found in a sigma orbital [18].

Their calculations also demonstrated that electrons found in orbitals which are not

localized directly between the two nuclei experience a steady increase in ionization rate

as internuclear distance grows. Again, these calculations were performed on the H2+

dimer and thus similar effects within our systems may or may not occur. Aside from the

initial differences in electronegativity between two different adjacent atoms within our

clusters, the situation is further complicated due to the various ionization potentials for

each atomic species, leading to varying charge states within the cluster and manifesting

as a dynamically changing intercluster potential landscape.

Previous work investigating the effects of enhanced ionization mechanisms in

small- and medium-sized clusters has been performed largely by two research groups.

Rost and coworkers have performed important theoretical work on rare-gas clusters

composed of 16-30 atoms [10] while experiments from Meiwes-Broer et al. have

concentrated on strong-field ionization of small Pt and Pb clusters [9,19]. Rost’s

75

theoretical work offers insight into several important properties of CREI in small clusters

[10]. Specifically, CREI is manifested most significantly in small clusters, as the

existence of an additional layer of atoms beyond the two aligned properly for the

ionization to occur would retard the outer ionization of any released electrons [20].

Secondly, CREI is not significantly frequency dependent, unlike the collective enhanced

ionization phenomena seen in larger clusters. Assuming the quasi-static approximation is

still somewhat relevant, CREI occurs under a wide range of laser frequencies, although

the actual value for Rc will change with respect to slight variations in cluster expansion

behavior under differing frequencies. Further, unlike dimers, clusters can also experience

CREI via circularly polarized light, due to the fact that there is a significant probability

that there will be two adjacent atoms aligned linearly with the laser polarization at any

given time. For further information, please see Chapter 1 of this work or the original

article from Sieschlag and Rost [10].

In order to further analyze the behavior of our small transition metal oxide

clusters upon irradiation with an ultrashort pulse of light, we have adjusted the laser

optics used in the creation and amplification of our laser pulse train to lengthen each

pulse from the standard 100fs to approximately 350fs, as described in the above

experimental section. The overall power was maintained at a constant 1.5mJ to provide

consistency between the experiments. The purpose of these studies was to determine

how laser pulse length would affect either of two possible ionization enhancement

mechanisms; CREI and/or CEMM. If CREI is the dominant ENIO mechanism, we may

or may not observe an increase in the maximum observable charge state. This is due to

the fact that if the internuclear distance within the cluster expands to the Rc (for electrons

in sigma orbitals) or ionization saturation is achieved (for off-axis orbitals) within the

100fs pulse, no further enhancement would be expected. However, if either of these

conditions was previously not met, widening the pulse may enable the cluster expansion

to proceed further and thus attain greater enhancement to the outer ionization from the

cluster. In the event that CEMM is providing significant enhancement to the ionization,

widening the pulse width may still allow the cluster to expand, altering the plasmon

frequency associated with the collective oscillations of any inner ionized electrons. The

76

expansion could potentially enable a resonance to occur between the cluster plasmon and

the frequency of the incident electric field, resulting in enhanced energy deposition and

finally cluster ionization. This effect was clearly demonstrated in homonuclear metal

clusters composed of 20 to 100 atoms by Meiwes-Broer et. al. and could provide some

further insight into the ionization mechanisms occurring in our experiments. It is also

worth noting that the IIM mechanism may play a more minor role in the cluster

ionization in longer pulse widths, as the charge-state on each atom would increase more

slowly, and the correlated cluster expansion would lower the influence of neighboring

atoms on one another. Shorter pulses yield less cluster expansion during equivalent

energy deposition and therefore allow IIM to be more significant.

The results from these experiments on our small clusters of NbxOy clusters are

shown in Figure 3-13. The graph represents the normalized populations of each

observable charge state for the niobium ions, with Nb+11

excluded due to insufficient

signal for accurate comparison and Nb+ omitted because of irresolvable overlap between

the multiphoton ionized species and those resulting from strong-field ionization. Each set

of data is normalized to the most intense peak in the spectrum, but the results are not

normalized to one another. There was no evidence of ions possessing charge states

beyond the Nb+11

species in either the long nor short pulse experiment and it is clear from

Figure 3-13 that the relative distributions of the observed ionic species are also

remarkably comparable. The significant drop in relative population of the Nb+2

thru Nb+5

ions and the more highly charged species is likely due to the fact that removing the 6th

electron from the niobium atom (the first electron from the 4p shell) requires a

significantly larger amount of energy (~102eV) than removing the electrons leading up to

the 5th

(50.55eV). Ionization enhancement mechanisms are likely required in order to

obtain sufficient energy from the strong field, but it appears that these mechanisms have

completed their influence within the original 100fs time frame represented by the short

pulse experiments. Due to the total lack of change in the maximum observed charge

states with respect to ionization pulse width, the clusters appear to be too small in size for

CEMM to have a significant effect on the ionization process.

77

To extend this study and search for ionization beyond the limits of our previously

observed charge states, we next took advantage of the flexibility inherent in our laser

vaporization source. By employing subtle changes in the source conditions, as well as

the source itself, we were able to produce a cluster distribution which contained and

centered at significantly larger clusters of transition metal oxides. Figure 3-14 contains a

graph demonstrating the shift to larger masses. This graphic representation shows the

total number of atoms per cluster and their relative populations within their individual

mass spectra, a much clearer and more useful depiction than the mass spectra themselves.

As shown in the graphic, the lighter cluster distribution is centered around clusters

composed of approximately 11 atoms while the heavier distribution contains significant

populations of clusters composed of up to 35 atoms. The heavy distribution is centered

around an average of 20 atoms, but remains fairly uniform in contributions from various

3-13: Normalized ion populations for the multiply charged species resulting from strong-field ionization

via a 350fs pulse (“long pulse” – black bars on the left) or a 100fs pulse (“short pulse” – red bars on the

right) of small niobium oxide clusters.

78

clusters throughout the spectrum. These sizes become significant in that enhanced

ionization from coherent electron motion was clearly demonstrated in homogeneous

metal clusters of approximately the same average number of atoms [19], as noted above.

Specifically, the Meiwes-Broer group reported observations of Pt+5

following irradiation

with a 140fs pulse but Pt+9

ion production with a 290fs pulse using 800nm light [14].

Despite our similar cluster size (~20 atoms vs. ~22 atoms, on average), similar

wavelength (624nm vs. 800nm), and similar pulse width expansion (100fs to 350fs vs.

140fs to 450fs), we did not observe any further ionization beyond the Nb+11

charge state,

as observed for both pulse widths. Further pulse expansion to ~600nm also revealed no

increase in maximum charge state. We therefore conclude that it is unlikely that CEM

plays a significant role in our experiments, as this mechanism is quite sensitive to

changes in pulse width.

3-14: Comparative, normalized distribution of small (lower, black line, Series 1) niobium oxide clusters

plotted with the heavier distribution (upper, red line, Series 2).

79

Because the expected ionization enhancement from CEMM is due to a shift in the

cluster plasmon frequency as a function of cluster expansion, we performed kinetic

energy release measurements to ensure that our clusters were, in fact, expanding to a

greater extent when irradiated with the longer laser pulse. The results of these

measurements are shown in Figure 3-15. As expected, the more gentle leading edge of

the 350fs pulse lead to slower outer ionization from the cluster and allowed the cluster to

expand to a greater extent than that observed with the 100fs pulse. This lead to larger

distances between cluster ions prior to Coulomb explosion and resulted in lower kinetic

energy obtained for each ion.

Data for several charge states of both the niobium and oxygen ions are provided

and demonstrate clear differences in the measured KER for each species. These species

in particular were chosen because their kinetic energy splitting in the mass signal was

well resolved within the same potential gradient in the mass spectrometer. Nb+6

was

omitted due to its similar m/z ratio with the large signal from the O+ ion. Similarly, O

+4

was not included due to its mass degeneracy with background signal from C+3

. Thus, we

have demonstrated the occurrence significant cluster expansion, yet we do not observe

3-15: Kinetic energy release (KER) values for selected niobium and oxygen atoms to demonstrate cluster

expansion during ionization via 100fs vs. 350fs pulse widths.

80

any enhancement (or degradation) in the maximum ionization state of the atoms within

the cluster as a result of various pulse widths.

Based on our observations, it is clear that there are no significant collective

electron effects participating in the ionization enhancement of our irradiated cluster

systems. There are several possible explanations for this. Despite the similar number of

atoms between our experiments and those performed previously by the Meiwes-Broer

group, it is the electron density which is most important in creating an environment in

which collective effects can be created. Given the ionic-covalent nature of the bonds

within our clusters, the overall electron density may not be sufficient in comparison to

metallically bound clusters of similar composition number. Calculating accurate

structures for clusters of this size is fairly demanding and as such, little theory has been

performed on clusters containing this many atoms. One group, however, has recently

performed theory work on vanadium oxide clusters in this size regime [21] and thus

progress on these calculations may soon be forthcoming.

A second potential explanation focuses on the heteronuclear nature of our

clusters. CEMM relies on the collective oscillation of electrons through the background

field of the cluster ions, and as such, an inhomogeneous field, such as that expected from

the multiple ionization of our heteronuclear clusters, likely fails to provide an ideal

environment for the creation of a plasmon, as there would be ionic “hot-spots”

throughout the cluster whenever the constituent atoms were ionized to differing charge

states. To our knowledge, theoretical work on this type of behavior has not been

published, and thus it would be worthwhile to investigate the possible influence of

various ionization mechanisms within heterogeneous clusters such as ours.

Thirdly, while the average number of constituent atoms per cluster in our

experiments was comparable to those reported by Meiwes-Broer and coworkers, the

maximum reported cluster sizes differ significantly. We did not observe the presence of

clusters containing more than 40 atoms within our distributions, whereas the studies on

pure metal clusters reported the production of clusters containing a maximum of ~100

atoms. As such, the coherent electron motion ionization enhancement reported in those

81

studies may be due to dynamics which only took place for the largest species in the

distribution and, as such, would not be observable in our smaller clusters.

Finally, differences in cluster expansion rate could factor in to the fact that we do

not observe ionization enhancement in the presence of a longer pulse width. The ionic-

covalent bonds which hold the transition-metal oxide clusters together are typically

shorter (~2Å) than the internuclear distances associated with the metallic bonding of pure

metal clusters (~3Å). Thus, the initial Coulomb repulsion between ion cores would be

stronger in the metal-oxide complexes, in addition to the fact that the less massive

oxygen atoms are typically located on the exterior of the cluster and would therefore

obtain proportionally larger amount of KE during repulsion. Despite the fact that the

metal-oxide clusters of comparable numbers of nuclei would initially exist in a more

compact structure than fully metallic counterparts, the heteronuclear clusters could also

undergo more rapid expansion and therefore grow to dimensions which allow a plasmon

resonance to occur within the short pulse width offered by the 100fs pulse experiments.

If this was the case, no improvement in ionization enhancement would be observed

utilizing a longer pulse width. In fact, Meiwes-Broer et al. observed [9] that upon

widening the pulse too much (typically 1000fs or so in their work) the maximum charge

states would actually decrease.

As discussed in the introductory chapter of this thesis, theoretical work regarding

strong-field ionization in molecules and clusters is limited due to the intense

computational workload inherent in dealing with complex multi-electron dynamics which

occur in polyatomic systems. To further complicate the matter, the ionization rates of

transition metal atoms are notoriously difficult to predict, as the multiple delocalized

valence electrons associated with transition metals prohibit the use of traditional single-

active electron approximations [22]. Significant screening can occur as the incident

electric field polarizes the atom and increases the potential barrier retarding the ejection

of valence electrons and thus lowers the field ionization rate below that which is

predicted by SAE models. Thus, any theoretical investigations would be fairly

complicated if a simple model could not be used in lieu of exact calculations.

Regardless, theoretical work on heteronuclear molecules and clusters with multivalent

82

atoms and drastically different electronegativities and ionization energies would certainly

be very interesting and pertinent to a variety of systems.

3.5 Conclusions

In conclusion, our strong-field (I~1015

W/cm2)ionization experiments on small

transition metal (Ti, V, Cr, Nb, Ta) clusters yielded a variety of maximum charge states,

seemingly correlated with the periodic trends in ionization energies associated with the

atoms which comprised the clusters themselves. All of the observed charge states extend

well beyond what was feasible based purely on the field ionization of the atomic species.

Therefore, enhanced ionization must be occurring within the cluster as a function of the

superposition of the external electric field and the internal potential landscape of the

cluster itself. We observed an increase in maximum charge state as a function of

increasing atomic mass for the Group Vb experiments while observing lower maximum

charge states for increasing mass for the Row IV species investigated. Each of these

findings is rationalized within the limits of the ionization energy data available in the

literature. Surprisingly, we find that charge states are created for each species which

correspond to the deposition of nearly identical amount of energy due to the laser-cluster

interactions, regardless of the identity of the transition metal constituting the cluster.

Further, we performed experiments investigating the effects of pulse width on

niobium oxide clusters of two different mass ranges in an attempt to qualify the

ionization enhancement phenomena which contributed to the creation of our highly

charged ions. However, we reported no difference in maximum observable charge state,

based on neither cluster size nor pulse width. Based on these observations, it was clear

that there were no significant contributions from collective electron motion within a

cluster plasmon. Hence, we concluded that the most likely ionization enhancement

mechanisms were IIM and CREI, and that the effects of CREI were completed within the

initial pulse width of 100fs.

83

3.6 References:

[1] Purnell, J., Snyder, E.M., Wei, S., Castleman Jr., A.W., Chem. Phys. Lett., 229 (4-5),

333-339 (1994).

[2] Snyder, E.M., Wei., S., Buzza, S.A., Castleman Jr., A.W., Chem. Phys. Lett., 248 (1-

2), 1-7 (1996).

[3] Snyder, E.M., Buzza, S.A., Castleman Jr., A.W., Phys. Rev. Lett., 77 (16), 3347-3350

(1996).

[4] McPherson, A., Thompson, B.D., Borisov, A.B., Boyer, K., Rhodes, C.K., Nature,

370 (6491), 631-634 (1994).


[6] Last, I., Jortner, J., Phys. Rev. A, 62 (1), 013201 (2000).


1182-1190 (1997).

[8] Ditmire, T., Donnelly, T., Rubenchik, A.M., Falcone, R.W., Perry, M.D., Phys. Rev.

A, 53 (5), 3379-3402 (1996).

[9] Koller, L., Schumacher, M., Kohn, J., Teuber, S., Tiggesbaumker, J., Meiwes-Broer,

K.H., Phys. Rev. Lett., 82 (19), 3783 (1999).


[11] Veniard, V., Taieb, R., Maquet, A., Phys. Rev. A, 65, 013202 (2002).

[12] Maruyama, S., Anderson, L.R., Smalley, R.E., Rev. Sci. Instrum. 61, 3696 (1990).

[13] CRC, Handbook of Chemistry and Physics, 89th Ed., 2008/09, editor D. Lide,

Cleveland, OH: CRC Press, p. 10-203/205.

[14] Radcliffe, P., Doppner, T., Schumacher, M., Teuber, S., Tiggesbaumker, J., Meiwes-

Broer, K.H., Contributions to Plasma Physics, 45 (5-6), 424-431 (2005).

[15] Corkum, P.B., Phys. Rev. Lett., 71, 1994 (1993).

[16] Ishikawa, K., Blenski, T., Phys. Rev. A, 62, 063204 (2000).

[17] Kjeldsen, T.K., Madsen, L.B., Hansen, J.P., Phys. Rev. A, 74, 035402 (2006).

[18] Kamta, G.L., Bandrauk, A.D., Phys. Rev A, 75, 041401(R) (2007).

84

[19] Schumacher, M., Teuber, S., Koller, L., Kohn, J., Tiggesbaumker, J., Meiwes-Broer,

K.H., Eur. Phys. J. D, 9 (1-4), Sp. Iss. SI, 411-414 (1999).


R77 (2006).

[21] JACS 129 (43) 13270-13276, (2007).


203402 (2004).

Chapter 4

Strong Field Ionization Studies of Homogenous Transition Metal Clusters

In a systematic attempt to experimentally further our knowledge regarding the

ionization mechanisms which are applicable to the irradiation of a small cluster with an

intense, 100fs pulse of light, we have performed strong-field ionization studies on small

homogeneous transition metal clusters. These studies serve as excellent comparisons to

the complementary work presented in Chapter 3, as niobium and tantalum oxide clusters

composed of similar numbers of atoms were well characterized therein. Here, we present

experimental observations regarding maximum charge states and discuss possible

implications regarding the strong-field interaction with the cluster and the subsequent

ionization mechanisms. It is shown that the maximum charge states created are identical

to those observed in the transition metal oxide cluster trials and that pulse width has no

observable effect on the maximum charging of these small clusters. Furthermore, the

ionization ignition and enhanced ionization mechanisms are proffered as the most likely

sources of the observed ionization behavior

4.1 Introduction

The interactions between intense pulses of femtosecond duration light and matter

have become the subject of a novel and exciting field of physics and chemistry. To date,

target materials have ranged from single atoms [1] to clusters [2] to transparent solids [3]

while the duration of the irradiative pulses have extended from nanoseconds [4] to

attoseconds [5] while spanning wavelengths from the IR [6], to the VUV [7] and beyond

to the x-ray regime [8]. Not surprisingly, changes in any of these factors can lead to

significant variations in the ionization behaviors within the target system. Further, it has

86

been discussed both in the previous chapter of this thesis and elsewhere [9] that the

maximum ionization state attainable via strong-field interactions can be greatly enhanced

by collective and/or cooperative behaviors within a multinuclear system (see Chapter 1

for details).

The majority of small homogeneous clusters which have been studied to date have

concentrated on rare-gas clusters (see, for example, the work of Castleman et al. [2] and

Siedschlag and Rost [10]) with some attention given to metallic clusters (notably the

work of Meiwes-Broer and coworkers [11]). In their simulations on strong-field

ionization of 16-30 atom rare gas clusters, Siedschlag and Rost observed enhanced

ionization primarily via ionization ignition (IIM) and the cluster equivalent of the

molecular enhanced ionization process (ENIO) (please see Ch.1 for a summary of these

mechanisms). Interestingly, the authors did not report any collective electron effects and

attributed this to the fact that the target clusters were too small to retain the inner ionized

electrons required for such behavior. Amongst many other observations, their studies

also showed a relative insensitivity of the ENIO mechanism to cluster size (Ar16-Ar30) as

well as the incident laser frequency (assuming the ionization/tunneling response of an

electron in a potential well occurs on a much faster time scale than the oscillatory motion

of the incident laser field: i.e. the quasi-static or adiabatic approximation).

Those observations are in contrast to the results from the experiments of Meiwes-

Broer et al. [11]. Specifically, in their studies of small (<100 atoms, average of ~20)

homogeneous platinum clusters, Meiwes-Broer and coworkers observe a dramatic effect

on ionization efficiency due to collective effects; namely the creation of a plasmon within

the cluster. They have also performed studies of other coinage metals [12] and observed

the same behavior; however, these later studies focused on clusters containing some

22,000 atoms and thus are not directly comparable to the work presented here.

Nonetheless, in both of these scenarios they attribute the ionization enhancement to the

preferential transfer of energy from the external field to the cluster upon attaining a

resonance between the collective motions of inner ionized electrons and the incident laser

pulse. This resonance is enabled via the dynamic frequency of the cluster plasmon,

which gradually lowers as the cluster expands (due to the Coulomb repulsion of the ion

87

cores initially created by the leading edge of the laser pulse) until it matches that of the

incident radiation. Thus, longer pulse widths (although pump-probe studies have

demonstrated this phenomenon as well) are required to allow the cluster time to expand

while still under the influence of the laser pulse.

This behavior is not at all unexpected, as other studies have shown the dynamic

polarizability of transition metal atoms [13] as well as clusters [14] to have significant

influence over their ionization rates and behaviors when exposed to strong electric fields.

Specifically, it was determined that the ionization rates of neither the atomic nor clustered

transition metal systems can be predicted by a single-active electron approach due to the

considerable influences of the characteristic delocalized electrons associated with these

elements. Dynamic screening due to non-adiabatic polarization of the valence electrons

leads to an inhibition of the ionization process [14]. In another manifestation of this

polarizability, recent studies have demonstrated that early transition metal clusters

(specifically Group Vb metals) exhibit ferroelectricity [15] (formation of a spontaneous

electric dipole) and ferromagnetism [16] at low temperatures. As such, the delocalized

electrons within transition metal clusters clearly manifest themselves as substantial

contributors to the energetic dynamics involved in the strong-field ionization of a metallic

system.

In this work, we present our findings regarding the strong-field ionization (SFI)

behavior of small, homonuclear clusters composed individually of niobium and tantalum

atoms. We utilized time-of-flight mass spectrometry to ascertain the highly ionized

products resulting from this ionization and the subsequent Coulomb explosion. Further,

the pulse width of the ultrashort ionization laser was extended to determine whether

collective electron effects played a significant role in the enhanced ionization we

observed. Comparisons are also made between the results of this work and the

heteronuclear studies reported in Chapter 3.

88

4.2 Experimental Details

The majority of pertinent experimental particulars have been provided in Chapter

2 but some additional steps were employed in the preparation of atomically pure

homogeneous clusters. It was vital that any source of oxygen contamination was

removed from the clustering gas (He), the gas lines, the sample rod, and the source itself,

as oxygen preferentially binds to the transition metals studied in these experiments. The

presence of oxygen can thus retard and/or eliminate the possibility of creating

homogeneous metal clusters. Thus, these sample preparation methods are discussed in

combination with a short review of the standard techniques used in our SFI studies of

clusters.

Briefly, a laser vaporization (LaVa) source was utilized in the creation of a

relatively narrow distribution of clusters composed of pure transition metals. Following

the production of the cluster beam (containing both ionic and neutral clusters) and

subsequent skimming to better define the dimensions of the beam itself, the clusters

encountered the time-of-flight mass spectrometer (TOF-MS). A static potential was

maintained across the ion extraction assembly, deflecting cluster ions. Shortly after

entering the extraction region, the remaining neutral clusters were ionized with an

ultrashort laser pulse.

The ionizing laser beam was supplied by a colliding pulse, mode-locked (CPM)

dye laser. Ultrashort pulses (100fs or 350fs) of broadband light centered at 624nm were

produced at 10Hz. Prior to crossing the cluster beam line, the femtosecond laser was

focused down to intensities of approximately 1x1015

Wcm-2

. The pulse train was focused

down to arrive about 0.8cm from the repeller plate (approximately halfway between the

repeller and extractor plates, ~1.65cm apart). Further, the axis of polarization for the

laser was aligned parallel with the direction of product ion propagation in the mass

spectrometer. The background pressure within the vacuum chamber was maintained

below 5x10-8

torr while rising to 5x10-6

torr while under operation.

Creating pure transition metal clusters required a meticulous approach to

cleanliness due to the fact that the transition metal atoms were much more likely to

89

cluster with carbon and oxygen atoms than they were other atoms of their own species

[17]. In the most general sense, this was due to the fact that both the carbon and oxygen

species were much more electronegative than the early transition metals studied herein.

Thus, the combination of an electronegative species (carbon or oxygen) and a slightly

electropositive species (a transition metal) lead to a preferential sharing of electrons and

more facile routes to both bonding and clustering. Pure metal clusters however, lack the

ability to form these ionic-covalent bonds. Rather, pure metal clusters are held together

with metallic bonding, in which electrons are delocalized and shared as they interact with

the positively charged metallic cores of the atoms being bound together. Therefore

improvements in both the clustering and cooling conditions for these experiments were

necessitated to create pure metal clusters. It should be noted that the following

procedures and methods were either adapted from or directly influenced by previously

published techniques, most specifically [18,19].

The first step in obtaining pure clusters was the elimination of species to which

the transition metals would preferentially bond with. To this end, several measures were

taken to eliminate any oxygen or carbon containing species from the reactant gas, target

metal rod, and surrounding cluster source. To reduce/eliminate the oxygen in the cooling

gas necessary for clustering, ultra pure (UHP, grade 6.0) helium was used in place of the

typical high purity helium. Unfortunately, despite the ultra high purity of this gas, there

were still some contaminants (specifically H2O) which needed to be eliminated. Further,

any gas line tubing used to connect the helium cylinder and the LaVa source represented

another potential source of oxygen. Thus, all connections and tubing were made from

stainless steel, affording several advantages. Stainless steel is more resistive to oxidation

than other metal options, such as copper, and thus reduces the chance of an oxide layer

forming within the walls of the sample lines and contaminating them. Teflon tubing is

typically an excellent alternative for these applications, but does not allow for the

application of intense heating, removing the option of baking the sample lines out to

remove any oxygen or water buildup. Further, the source typically must be operated for

30-120 minutes before pure clusters were produced. This was attributed to oxidation on

the surface of the transition metal rod, as it has been found that oxygen atoms may be

90

embedded several monolayers deep within the crystal structure and this oxygen must be

removed via laser ablation to eliminate it.

The implementation of stainless steel sample lines also enabled the following

modifications and procedures to be incorporated. First, a section of the new stainless

steel tubing was twisted into a coil comprised of 5 full turns of the tubing with the inlet

and outlet ends of the tubing at the top of the coil. The coil was wrapped tightly enough

that it could fit into a small Dewar container. During operation, this Dewar was filled

with liquid nitrogen (~77K/-321oF/-196

oC) to act as a cold sink and freeze any

contaminants (especially H2O) which may reside in the ultra-pure helium and could

introduce oxygen or carbon into the system. It should be noted, lengthy operation in this

manner can lead to enough ice buildup that the gas line becomes clogged, at which time

the tubing must be warmed back to room temperature and the steps delineated below

must be followed to clean the tubing and remove the water. Note: any time the stainless

steel sample line experiences a significant increase in temperature, it should be vented

while being continuously purged with UHP helium. Taking these precautions will ensure

the line remains free from exposure to (and contamination from) atmosphere while

preventing any potential explosions which could result from the rapid expansion of the

evaporating (or subliming) frozen contaminant gases.

Prior to operation, and on the occasion of a clog, the Dewar was removed and the

entire length of sample line was baked out using an acetylene torch with the intent of

desorbing any undesirable species from the interior of the tubing. All joints were sealed

tightly with the exception of the final coupling between the tubing and the inlet into the

chamber itself (to allow gas to escape during heating and expansion) and, in the presence

of a continuous flow of UHP helium, the line was baked out for 5-10 minutes to remove

any water, oxygen, or other contaminant species which may have built up on the inner

walls of the sample line. Following the bake-out, the line was continually purged with

the ultra-pure helium to aid in cooling before the final coupling was tightened and the

sample line sealed. Thus, the majority of oxygen containing contaminants were removed

from the sample line.

91

In the aforementioned heteronuclear transition metal oxide studies, a sample rod

of the transition metal of choice was ablated using the second harmonic (532nm) of a

Nd:YAG nanosecond laser operating at typical powers of 2-4 watts while a solenoid

pulsed nozzle delivered a mixture of gas (~5% oxygen seeded in pure helium). As the

laser ablated the sample rod it created a plasma with which the pulse of gas contributed to

and interacted with, allowing for the formation of clusters as this dense mixture of ions

interacted and collisionally cooled. In the present experiments, these same conditions

were required and provided; however, the nature of the clustering process was less facile

due to the lack of oxygen atoms to aid in both the clustering and cooling aspects of the

procedure. Thus, in order for the creation of neat clusters to take place, the source

geometry and operating conditions were slightly modified.

In this vein, the second step in producing pure clusters involved the

aforementioned geometrical and operational modifications to the laser vaporization

source. In the past, several source parameters have been found to be vital to the

clustering of certain atomic species, as well as to adjust the extent of clustering in other

systems. These parameters affected one or both of two things; namely, the number of

collisions/interactions between the ionized materials within the source and the extent to

which energy was removed from these systems to aid in creating stable clusters.

Physically, these conditions were usually modified by increasing the backing pressure of

the sample gas, substituting larger inert atomic species for use as a carrier gas, changing

the dimensions of the waiting room area within the source, and altering the diameter,

shape, and/or length of the expansion nozzle. Further, the expansion nozzle and/or the

entire source can be externally cooled by a circulating liquid nitrogen line to aid in

cooling and stabilization of the cluster species, although incorporating that method into

the current work would be extremely arduous due to structural restrictions. Regardless,

creating clusters from species which typically resist clustering for energetic reasons

required a set of source conditions that increased the number of collisions between the

target atoms while removing as much energy from the clusters, once formed, as possible.

It is worth mentioning that a formula has previously been developed to aid in

quantitatively relating several of these factors. Referred to as the Hagena formula [20], it

92

can be useful in determining methods of improving clustering conditions and the

approximate size clusters which will be produced. This equation is based on

experimental data and can be useful as a guideline in determining the potential extent of

clustering as it results from a free jet expansion under specific experimental conditions.

However, the Hagena equation was not fully incorporated into the methods and approach

described here, therefore further improvements may be feasible.

For these particular experiments, aside from varying the backing pressure of the

helium cooling gas, a significant change was made to the dimensions of the expansion

nozzle in the LaVa source, which resulted both in an elevated internal source pressure as

well as improved collisional cooling conditions. By replacing the typical bi-conical

nozzle with a linear tube of greater length and narrower inner diameter (see illustrations

in Figure 4-1), the pressure inside the waiting area was increased and collisions with the

expansion nozzle, acting as a heat sink, were also greatly increased. Specifically, an

expansion nozzle which was 38.5mm long and had an inner diameter of 1.5mm

throughout its entire length was fabricated and used in these experiments. Thus, the

production of (nearly) pure transition metal clusters was performed.

Based on the reasonable successes experienced with the transition metal oxide

studies, neutral mass spectra were obtained for the pure clusters studied herein. As

before, this was accomplished by defocusing the CPM ionization beam to the point at

which single ionization events dominated the energetic processes and the ionized species

were detected via the TOF-MS. These spectra and the ion data resulting from strong-

field ionization are presented in the following section.

93

4.3 Results

This section contains the data resulting from these experiments on SFI of

homogeneous metal clusters, including some rudimentary analysis to explain the data.

The following figures present the neutral cluster (obtained via defocused CPM with

intensities of ~1012

W/cm2) and strong-field (~10

15 W/cm

2) ionized atomic mass spectra

results. The mass spectra depicting the highly charged ions have been somewhat

truncated to maximize the clarity of the important species; namely the highest charge

states of the transition metals themselves. Further, for each of the multiply-charged

product spectra, dashed lines have been provided to guide the eye, each of which is

positioned at the exact m/z ratio predicted by an overall calibration line. Treatments such

4-1: Illustrative depiction of the LaVa source change required for the creation of pure metal clusters. The

source used in previous experiments (a) remained primarily the same, with the exception of the

implementation of a different expansion nozzle (b). The new nozzle was slightly longer (38.5mm) and

much narrower (1.5mm) throughout its entire length. This nozzle also decreased the size of the waiting

room, increased the pressure inside the source, and aided in removing additional energy from the system to

stabilize the pure metal clusters. Several important components of the source are labeled for clarity.

94

as these proved highly useful for identification of the Maximum Observable Charge State

(MOCS) for each experiment.

4.3.1 Pure Niobium Cluster Studies

The first of two sets of pure transition metal clusters studied within this work

were composed of niobium atoms. Figure 4-2 contains a mass spectrum of the neutral

clusters created by the laser vaporization source. The figure is a combination of two

spectra, as two different deflector plate voltages were required to observe the lighter and

heavier cluster species. This was done solely to observe the entire cluster distribution

and such changes did not affect the strong-field ionization aspect of the experiments. As

shown in the figure, the majority of niobium clusters contained between 5 and 17 atoms,

with very little influence from clusters possessing more than 26 atoms. As evidenced on

the earliest peaks in the spectrum, there was still some oxygen contamination on the

clusters, despite the rigorous steps taken to eliminate its presence. This was not

unexpected, as most published “pure” homogeneous clusters of transition metals still

contain some small amount of oxygen [19]. However, it appeared that not more than one

oxygen atom was found on our first few clusters and this was unlikely to drastically alter

the metallic bonding character of the clusters, especially for the larger species.

95

Figure 4-3 contains the subsequent ion spectrum of the products resulting from

exposing the pure clusters to an intense 100fs pulse. As detailed in Chapter 3, there was

some contamination from background gases which resulted in the observation of carbon,

oxygen, and nitrogen ions, but the levels were quite low and did not interfere with species

identification. The highest observable charge state for the transition metal was Nb+11

,

seen as a small shoulder to the right of the O+2

signal. The calculated m/z ratios are

indicated by the dashed lines which highlight the presences of our highly charged ions.

KER splittings are clearly resolved for the Nb+3

through Nb+7

species. Figure 4-4 shows

the resulting ion products upon ionization via a 350fs pulse, and the MOCS there was

also Nb+11

.

4-2: Typical cluster distribution for the neutral homogeneous niobium species. Note that this spectrum

was obtained via the defocused CPM beam by translating the focusing lens approximately 3cm away from

the maximum focus position, thus reducing the laser intensity to ~1012 W/cm2 thus minimizing multiple

ionization events to enhance single ionization. The figure is a combination of two spectra to enable a

complete depiction of the entire cluster distribution.

96

4.3.2 Pure Tantalum Cluster Studies

Like Figure 4-2 for the neutral niobium clusters, the spectrum shown in Figure 4-

5 was also the resulting combination of two distributions of neutral pure tantalum

clusters, each obtained using a slightly different deflector voltage in order to present a

more complete depiction of the cluster species present in our molecular beam. As shown

in the figure, the majority of our tantalum clusters contained fewer than 22 total atoms.

Similarly to the pure niobium clusters, there was some evidence of a single oxygen atom

bound to several of the smaller clusters. Interestingly, there was also evidence of

multiply charged clusters in this mass spectrum. The significantly larger size and

metallic bonding nature associated with these clusters allows for the loss of multiple

electrons due to multiphoton ionization without necessarily resulting in the fragmentation

of the entire cluster [21]. Evidenced in the mass spectrum, it appeared that the clustering

of a minimum of 9 tantalum atoms were required for the manifestation of this

phenomenon.

97

4-3: Mass spectrum resulting from the SFI of neutral homogeneous niobium clusters via a 100fs laser pulse.

Note the maximum observable charge state is the Nb+11 ion.

4-4: Mass spectrum resulting from the SFI of neutral homogeneous niobium clusters via a 350fs laser pulse.

Note the maximum observable charge state is the Nb+11 ion.

98

Figures 4-6 and 4-7 contain the resulting ion spectra following cluster ionization

with an intense (I~1x1015

W/cm2) 100fs and 350fs pulse, respectively. Dashed lines have

been provided to guide the eye in identifying specific species. It appeared that there was

some evidence of the Ta+11

species while the Ta+10

was clearly present in both spectra.

The spectrum resulting from the 100fs ionization pulse was taken using the short field

free region and a voltage gradient which provided ample opportunity for KER splitting to

be appreciably manifested. Figure 4-7, showing ionization from the 350fs pulse, was

obtained using the long reflectron field-free region in conjunction with an Einzel lens

which yielded improved mass separation but sacrificed any available KER data.

4-5: Typical cluster distribution for the neutral homogeneous tantalum species. Note that this spectrum

was obtained via the defocused CPM beam and is a combination of two spectra to enable a complete

depiction of the entire cluster distribution.

99

4-6: Mass spectrum resulting from the SFI of neutral homogeneous tantalum clusters via a 100fs laser

pulse. Note the maximum observable charge state is the Ta+11 ion.

4-7: Mass spectrum resulting from the SFI of neutral homogeneous tantalum clusters via a 350fs laser pulse. Note

the maximum observable charge state is the Ta+11 ion.

100

4.4 Analysis and Discussion

The focused laser intensity for these experiments approached 1015

W/cm2, which

yielded a maximum ponderomotive potential of UP ~ 36eV. The experiments were

performed within the 1>γ>0 regime in which tunneling ionization and strong-field effects

in general were expected to become important mechanisms in the electromagnetic field-

matter interaction. The initial ionization potentials for the niobium clusters in our

experiments have previously been determined experimentally [22] to range between

6.2eV (for Nb2) to 4.53 (for Nb15) while the first IP for a lone niobium atom is 6.76eV.

In fact, based purely on a single active electron approach, and neglecting all multi-

electron screening processes, it appears that the first 3 or 4 valence electrons could easily

be removed from a niobium atom (or a tantalum atom) via simple field ionization.

However, in our experiments with a 100fs pulse width we observed the

production of Nb+11

and Ta+11

ions as a result of strong field ionization! This indicated

ionization well beyond the valence shell of each species and clearly beyond any simple

approximations based on field ionization alone. Unfortunately, attempts to perform

strong-field ionization on the monotonic metals were unsuccessful and thus could not be

produced for comparison to the cluster studies. We expect that the difficulty in the

atomic ionization study of the metals is similar to that which makes mass-selected cluster

experiments so difficult; namely the inability of our laser vaporization source to produce

enough total quantity of the target atom to allow appreciable observation of the resulting

ion signal. Regardless, it is obvious that the clustered nature of our chosen targets plays

an integral role in enhancing the ionization behavior we observed.

The aforementioned delocalized electron character of metal clusters could play an

important role in their ionization behavior insofar as the bonding electrons are easily

ionized. Thus these electrons would be available for participation in ionization

enhancement mechanisms, assuming they remain inner ionized and are not immediately

ejected away from the influence of the cluster nuclei. However, it was unlikely that these

first few electrons were retained within the confines of our clusters, based purely on their

small size [9]. Further, it has been demonstrated that electron-ion recollision effects play

101

a sufficiently minor role in the strong field ionization of small clusters [23] that they may

ultimately be neglected in the following discussion and analysis. Thus, we focus on the

influences of IIM, ENIO, and CEMM as they related to our target cluster systems.

Further, we discuss how their individual manifestations could be affected by the different

cluster characteristics embodied by our Group Vb transition metal clusters, the small

platinum cluster investigated by Meiwes-Broer and coworkers, and the metal-oxide

species discussed in Chapter 3.

The influences of IIM are generally thought to be universal, in that the inner

electric potential landscape within the confines of the cluster itself is constantly changing

as ionic cores within the cluster begin to be born as a result of field ionization (initially)

and ionization enhancement mechanisms (later). Thus, the significance of this effect is

often glossed over and assumed to be present while not existing as the main mechanism

of interest. For the most part, this approach was also taken in these discussions, as a lack

of theoretical treatment makes such arguments decidedly difficult. Thus, our attentions

turned to the subsequent ionization enhancement mechanism which appeared to be

manifested in these studies; ENIO.

ENIO was the most likely mechanism responsible for the significant enhanced

ionization (EI) observed in these experiments and we offer several experimental details

which led to this conclusion. From our experiments, we consistently observed identical

maximum charge states for each of our two cluster species in the presence of various

ionization laser pulse widths. In cases where coherent electron motion is a potential EI

mechanism, longer pulse lengths have invariably led to steady increases in maximum

charge state [24] as the cluster has the opportunity to expand and bring its plasmon

frequency into resonance with that of the incident laser field. This plasmon is based on

the same Mie frequency attributed to larger clusters and nanoparticles, and it is dependent

on the size, electron density, shape, etc of the system. In support of this, the bulk of the

reported experiments performed on small to medium sized clusters observe EI resulting

from CEM, which is indicated by increased maximum ionization states being created by

widening the pulse width from ~100fs to 3-4 times this width.

102

Our lack of change in max charge state indicated that our EI is likely completed

within the shorter pulse time and therefore had little dependence upon pulse width,

assuming the pulse was of sufficient duration to allow the necessary expansion for the

ENIO mechanism to proceed. It has been shown that in order for ENIO to proceed at an

enhanced rate, the internuclear distance between two neighboring atoms must approach a

critical internuclear distance, Rc. This Rc is attained via the cluster expansion which

occurs based on the Coulombic repulsion experienced by atoms within the cluster once

field ionization has created the initial ion cores. This phenomenon was first found to

manifest itself in dimers but has since been extended to small molecules and clusters [9].

For electrons localized in sigma orbitals, this mechanism has the greatest contribution at

interatomic distances of approximately 2-3 times the ground state distance [10]. Further,

it is known that the expansion required to reach the Rc for ENIO, is smaller than that

needed for CEM to come into resonance with the electric field (dependent upon the

frequency of the exciting laser pulse, of course) [9]. Thus, the Rc for our clusters could

be reached during the 100fs pulse and due to a lack of collective effects, no further EI

occurs in the presence of a longer pulse.

Another argument in favor of ENIO and against CEM focuses on the small

dimensions of our target clusters. In general, plasmon effects are more readily realized in

larger systems in which inner electron ionization dominates. Our clusters were small

enough that the majority of electrons which were ionized were carried outside the

influence of the cluster itself by the electric field and were immediately outer ionized,

inhibiting the formation of a substantial plasma within the cluster. These smaller

dimensions are ideal for ENIO, however, in that any electron which was ionized could

likely escape the cluster with a minimal chance of encountering the restraining influence

of another ionic core, due to the lack of an extensive shell structure within the cluster.

Further, it is clear that EI is occurring within the 100fs pulses, as Nb+11

and Ta+11

ions are created during that short pulse, and even with our somewhat higher frequency

(compared to the typical 800nm from a Ti:saph laser), it is unlikely that enough cluster

expansion is occurring for the creation of a plasmon resonance. In coming to these

conclusions, we present a stark contrast in EI mechanism to that observed in one of the

103

few comparable systems reported to date, platinum clusters. While not directly

comparable with respect to laser conditions and cluster composition, both sets of

experiments are relatively similar. In spite of this, the results of the two are quite

different.

Specifically, Meiwes-Broer and coworkers observed the creation of Pt+5

ions as a

result of ionization using a 140fs, 5mJ pulse while a 290fs pulse of the same energy

yielded ions as highly charged as Pt+9

, with maximum charging (Pt+11

for this energy)

resulting from a 600fs pulse. One significant difference in the two target systems

between these two sets of experiments, aside from the identity of the constituent

transition metals, is the sizes of the clusters themselves. Meiwes-Broer et al. approximate

(based on observed cationic and anionic species) that their clusters contain an average of

20 to 100 total platinum atoms. On the contrary, as shown in Figs. 4-2 and 4-5, our

clusters contained an average of ~13 atoms and we do not observe clusters containing

more than 25 total atoms for either species. All other things considered equal, this onset

of CEM could be attributed to the sizes of the clusters themselves. The electron densities

of niobium and tantalum clusters are on the order of those associated with platinum

clusters of equal size, and thus no advantage is garnered there.

As metallic clusters grow in size, they tend to maintain relatively spherical shapes

and develop layers which would, according to some authors [9], hinder the outer

ionization of electrons which are released via the ENIO mechanism. Based on structures

calculated by Fa, Luo, and Dong [16] on pure neutral tantalum clusters (it has been

shown that niobium and tantalum clusters are extremely similar, most certainly for the

purposes here), our target clusters are roughly symmetric and spherical, like the larger

clusters would be, but have not grown in size enough to form multiple shells of atoms

within the cluster structure. Thus, it is unlikely that our clusters are of sufficient size for

appreciable inner ionization to occur and therefore CEM effects are negligible. This is in

contrast to the published work on platinum clusters which have evidently reached the size

threshold wherein a substantial cluster plasmon can be formed. Further experiments and

theoretical treatments will help to clarify this potential behavior, but nonetheless we treat

104

these observations as initial experimental evidence that the EI phenomena manifested in

systems of similar sizes can be substantially, and observably, different.

In keeping with this interpretation, it is interesting to discuss the presence of a

critical internuclear distance with respect to the EI of these clusters. As discussed in the

Introduction (Chapter 1), for electrons localized directly between two atoms, this Rc

value represents the internuclear distance which would lead to maximum ionization

enhancement. However, for those electrons located “off-axis”, i.e. not directly between

the two nuclei being addressed, the increase in ionization rate grows monotonically as the

internuclear distance grows [26]. The electrons in our clusters are quite delocalized,

especially the valence electrons, and thus are unlikely to be concentrated directly between

two atoms. Therefore, their ionization rate should continue to increase as interatomic

distance increases, as it would in a 350fs pulse. Thus, based on the lack of further

ionization in the presence of a longer pulse width, it is likely that our clusters expand

sufficiently within the 100fs pulse that, if it exists, the Rc is reached while the ionization

rate from off-axis orbitals has clearly become saturated as well.

Assuming the above discussion is true, and that our small metal clusters are

indeed undergoing ionization enhancement via the ENIO and IIM mechanisms, it is

interesting to compare these studies with those discussed in Chapter 3 which dealt with

the strong-field ionization of early transition metal oxide clusters. Unlike the relatively

localized bonding electrons associated with those covalently bound clusters, the metallic

bonding of pure metals results in the significant delocalization of valence electrons within

the cluster, possibly leading to substantial differences in ionization behavior and

dynamics. However, a quick comparison reveals that the maximum charge states (and

lack of change in the presence of various pulse widths) are remarkably similar for the

pure niobium and niobium oxide clusters as well as the companion tantalum studies!

For the niobium (and tantalum) oxide we observe the creation of the M+11

ion;

identical to those produced from the irradiation of pure metal clusters. As evidenced in

the discussion of enhanced ionization mechanisms found in Chapter 1, the attributes of a

molecule or cluster can have a dramatic effect on the EI behavior which can occur upon

exposure to a strong electric field. Thus our agreement is rather interesting, since these

105

cluster systems certainly are quite different, not only in their structures, composition,

bonding character, and interatomic distances, but also the number of valence electrons

available for participation in ionization enhancement. In light of the significant

differences related to these two types of clusters, one would expect the behaviors of

ENIO as well as IIM to manifest somewhat differently, and certainly not result in the

same MOCS.

Despite the fact that each set of cluster experiments was performed on a

distribution containing similar numbers of atoms, the identity of the constituent atoms

and the nature of the bonding within the cluster create a substantially different

environment in which the strong-field can influence the ionization dynamics of the

cluster. By increasing the number of transition metal atoms and eliminating the oxygen

species, we have essentially increased the overall number of electrons contained within

the clusters themselves. Further, the metallic bonding nature of the pure metal clusters

results in larger interatomic distance and thus also changes the dimensions of the cluster.

For this reason, the overall increase in the total number of available electrons cannot

necessarily be correlated with an increase in the electron density of the target.

One of the significant downsides to working with transition metal clusters,

however, is the relative difficulty in modeling not only their electronic behavior, but

simply their structures as well. These difficulties arise not only due to the multi-valence

electronic nature of the transition metal atoms, but also the rapidly increasing number of

feasible isomers possible as the total number of atoms within the cluster grows.

Recently, gas-phase experimental studies of small homogeneous vanadium [27,28],

niobium [29], and tantalum [30] clusters were reported using the FELIX (Free Electron

Laser for Infrared eXperiments) facility to perform high resolution infrared multiple

photon dissociation (IR-MPD) experiments. DFT calculations were supplied for the

vanadium and niobium studies and excellent structural agreement was found between

theory and experiment for the Vn (n=3-23) cations as well as the Nbn (n=5-9) neutral and

cationic clusters. In these studies, it was found that all three species of cluster produced

very similar vibrational spectra in their cationic form, especially for clusters containing 6,

7, 13, 15, and 17 atoms and the cluster growth patterns appeared consistent for the entire

106

group. These experiments represent a much needed advance in the study of transition

metal cluster structure and may aid in the future development of accurate models for the

multiple ionizations studied and reported herein.

By utilizing this data, we can offer some discussion regarding the effects of

cluster structure on ionization behavior. For example, the average bond distance between

two niobium atoms within a Nb13 cluster is in the range 2.39-3.12 Å [31], while the Nb-O

bond length in a Nb4O10+ cluster is on the order of 2.0(bridging)-1.9(terminal)Å [32].

These are, of course, simply baseline numbers for the lowest energy isomers and serve

simply to make a point, as the wide range of cluster sizes and inherent isomers found

within an actual experiment make real comparisons somewhat ambiguous. In light of the

IIM phenomenon, one would expect that the reduction in potential barrier between

neighboring ions would be more significant in the heteronuclear clusters possessing

shorter bond lengths, based on a simple, qualitative view of Coulomb’s law. Further, as

discuss in Chapter 3, the production of identically charged oxygen and transition metal

atoms does not occur with identical amounts of energy. Specifically, the removal of the

5th electron from a niobium atom requires less energy (~24eV) than the removal of the 3

rd

electron from a neighboring oxygen atom (~35eV). One can surmise, therefore, that the

O+3

nucleus would not have as large of an electron withdrawing effect on a neighboring

niobium ion as an Nb+5

ionic core would. Therefore, it appears that IIM would favor the

pure metal clusters based on the likely higher charged neighbors, but simultaneously

would suffer from the increased interionic distance characteristic of metallically bound

clusters. Again, these discussions are speculative, but clearly some theoretical

simulations might prove quite enlightening and worthwhile. To the best of our

knowledge, and as of this writing, none have been reported.

Regarding the effects of the differing structures and cluster composition on the

ENIO mechanism in these studies, there have not been any published calculations

performed which could lend insight into the variations in dynamics with regard to this

phenomenon’s manifestation. However, based on the fundamental mechanism which

enables ENIO to occur, namely the favorable balance of shifted potential barriers

between two nuclei based on internuclear distance and the superimposed external electric

107

field, one can postulate how the dynamics of ENIO would vary between homo- and

heteronuclear clusters. For instance, in the majority of the transition metal oxide clusters,

the metal units are generally localized within the interior of the cluster while the oxygen

species tend to occupy bridging locations between niobium atoms or orient themselves in

terminal positions furthest from the center of the cluster. Interestingly, it has recently

been theoretically demonstrated [33] that in very short, few-cycle laser pulses, the

orientation of a molecular dipole (in a heteronuclear dimer, He-H in this case) with

respect to the polarization of the incident electric field has a significant impact on the rate

of outer ionization. However, these effects are expected to be negligible upon exposure

to longer pulses, even those as short as the 100fs pulses utilized here. Thus, the effects of

having an inner metallic character and an outer oxygen population are not expected to be

significant as a direct result of the dipoles formed between the atoms in the cluster.

On the other hand, based on the structural information for the transition metal

clusters, it is straightforward to assume that the lower-massed oxygen atoms would

accelerate away from the center of the cluster more quickly than the centrally located

transition metal atoms. On the contrary, for homogeneous systems, the outer nuclei

would expand the diameter of the cluster at a slower rate due to the equivalency of their

masses. Based purely on this Coulombic argument, and assuming that ENIO proceeds

with the same efficiency when an electron is localized between two nuclei of differing

species as it would in the presence of matched ions, then Rc could be attained earlier in

the expansion of the heteronuclear clusters. However, even if this is the case, it is clear

that Rc is reached for both types of systems within the first 100fs of their exposure to the

external field, as they reach the same MOCS.

4.5 Conclusions

We report the results of strong-field ionization experiments on small (<30 atom)

homogeneous Group Vb transition metal clusters composed of either niobium or

tantalum. In both cases, we observe the creation of the M+11

ion under two different laser

108

pulse width conditions, possibly indicating that ionization was completed within the first

100fs of the laser-cluster interaction. We have initially attributed this behavior to the

ENIO mechanism, and thereby assume a lack of CEM effects, which is in contrast to the

mechanism previously reported [11] for experiments performed on small late-transition

metal clusters. The size distribution for our target systems is slightly smaller than the

previous work and this may play a significant role in the onset of these two EI

phenomena.

Further, upon comparison to the transition metal oxide clusters presented in

Chapter 3, we find that the metal components reach the same MOCS value. This result

was unexpected for the reasons discussed above and have inspired the performance of the

transition metal-carbide studies described in Chapter 5. Based on the mechanisms

typically attributed to the enhancement of ionization within small molecules and clusters,

one would anticipate that cluster environment would have noticeable effects on the

ionization of the composing atomic species. We do not find this to be the case and in the

absence of complementary theoretical work, can offer no rationale behind the agreement

beyond informed speculation.

109

4.6 References

[1] Codling, K., Frasinski, L.J., J. Phys. B, 26, 783 (1993).

[2] Purnell, J., Snyder, E.M., Wei, S., Castleman Jr., A.W., Chem. Phys. Lett. 229 (4-5),

333-339 (1994); Snyder, E.M., Wei., S., Buzza, S.A., Castleman Jr., A.W., Chem. Phys.

Lett., 248 (1-2), 1-7 (1996); Snyder, E.M., Buzza, S.A., Castleman Jr., A.W., Phys. Rev.

Lett., 77 (16), 3347-3350 (1996).

[3] Bhardwaj, V.R., Rajeev, P.P., Corkum, P.B., Rayner, D.M., J. Phys. B: At. Mol. Opt.

Phys. 39, S397-S407 (2006).

[4] Kong, X.L., Luo, X.L., Niu, D.M., Li, H.Y., Chem. Phys. Lett., 388 (1-3), 139-143

(2004).

[5] Okino, T., Yamanouchi, K., Shimizu, T., Furusawa, K., Hasegawa, H., Nabekawa, Y.,

Midorikawa, K., Chem. Phys. Lett., 432 (1-3), 68-73 (2006).

[6] Ditmire, T., Donnelly, T., Rubenchik, A.M., Falcone, R.W., Perry, M.D., Phys. Rev.

A, 53, 3379 (1996).

[7] Wabnitz, H., Bittner, L., de Castro, A.R.B., Dohrmann, R., Gurtler, P., Laarmann, T.,

Laasch, W., Schultz, J., Swiderski, A., von Haeften, K., Moller, T., Faatz, B., Fateev, A.,

Feldhaus, J., Gerth, C., Hahn, U., Saldin, E., Schneidmiller, E., Sytchev, K., Tiedtke, K.,

Treusch, R., Yurkov, M., Nature, 420 (6915), 482-485 (2002).

[8] Makris, M.G., Lambropoulos, P., Mihelic, A., Phys. Rev. Lett., 102 (3), 033002

(2009); Jurek, Z., Faigel, G., Tegze, M., Eur. Phys. J. D, 29, 217-229 (2004).

[9] There are many excellent reviews on the topic, most recently published are Saalmann,

U., Siedschlag, Ch., Rost, J.M., J. Phys. B: At. Mol. Opt. Phys., 39, R39-R77 (2006);

Krainov, V.P., Smirnov, B.M., Smirnov, M.B., Physics-Uspekhi, 50 (9), 907-931 (2007).


[11] Schumacher, M., Teuber, S., Koller, L., Kohn, J., Tiggesbaumker, J., Meiwes-Broer,

K.H., Eur. Phys. J. D, 9 (1-4), Sp. Iss. SI, 411-414 (1999).

[12] Radcliffe, P., Doppner, T., Schumacher, M., Teuber, S., Tiggesbaumker, J., Meiwes-

Broer, K.H., Contributions to Plasma Physics, 45 (5-6), 424-431 (2005).

110


213003 (2004).


203402 (2004).

[15] Moro, R., Xu, X., Shuangye, Y., de Heer, W.A., SCIENCE, 300, 1265-1269 (2003).

[16] Fa, W., Luo, C., Dong, J., J. Chem. Phys., 125, 114305 (2006).

[17] Most general chemistry and all inorganic chemistry textbooks cover this material.

[18] Heiz, U., Vanolli, F., Trento, L., Schneider, W.D., Rev. Sci. Instrum. 68 (5), 1990-

1991 (1997).

[19] Knickelbein, M.B., Yang, S., Riley, S.J., J. Chem. Phys., 93 (1), 94-104 (1990).

[20] Hagena, O., Rev. Sci. Instrum. 63 (4), 2374-2379 (1992).

[21] Delley, B., J. Phys. C., 17, L551 (1984).

[22] Knickelbein, M., Yang, S., J. Chem. Phys., 93 (8), 5760 (1990).

[23] Ishikawa, K., Blenski, T., Phys. Rev. A, 62, 063204 (2000).


K.H., Phys. Rev. Lett., 82 (19), 3783 (1999).


[26] Kamta, G.L., Bandrauk, A.D., Phys. Rev. A, 75, 041401(R) (2007).

[27] Fielicke, A., Kirilyuk, A., Ratcsh, C., Behler, J., Scheffler, M., von Helden, G.,

Meijer, G., Phys. Rev. Lett. 93, 023401 (2004).

[28] Ratcsh, C., Fielicke, A., Kirilyuk, A., Behler, J., von Helden, G., Meijer, G.,

Scheffler, M., J. Chem. Phys. 122, 124302 (2005).

[29] Fielicke, A., Ratsch, C., von Helden, G., Meijer, G., J. Chem. Phys. 127, 234306

(2007).

[30] Gruene, P., Fielicke, A., Meijer, G., J. Chem. Phys. 127, 234307 (2007).

[31] Kumar, V., Kawazoe, Y., Phys. Rev. B, 65, 125403 (2002).

[32] Fielicke, A., Meijer, G., von Helden, G., JACS, 125 (12), 3659-3667 (2003).

[33] Kamta, G.L., Bandrauk, A.D., Phys. Rev. Lett., 94, 203003 (2005).

Chapter 5

Strong-Field Ionization Studies of Transition Metal Carbide Clusters

In this chapter we present data representing further investigation into the

ionization behavior of heteronuclear clusters upon exposure to strong optical fields. A

similar approach is adopted from the work performed in Chapter 3, but the target clusters

are composed of transition metals and carbon atoms rather than oxygen. In performing

these experiments, we had hoped to observe some variation in ionization dynamics based

on the change in electronegativity of carbon versus oxygen. The work shown in Chapter

3 demonstrated that the identity of the transition metal portion of the target cluster was

pivotal in the extent to which ionization progressed for said metal atoms. Although it is

clear that the clustered nature of the target species heavily influenced the enhanced

ionization behavior which was observed, the role of the oxygen atoms within the clusters

was ambiguous at best. By “replacing” the highly electronegative oxygen component

with a significantly less electronegative element, we sought to observe some variation in

the Maximum Observable Charge States (MOCS) created for the transition metal atoms.

As will be shown in this chapter, however, this was not the case. In fact, we report very

similar, or identical in some cases, MOCS values for each of the transition metal

experiments performed for which there was an oxide analogue.

5.1 Introduction

As discussed in the previous chapters, the ionization behavior of small

heteronuclear systems is a somewhat unexplored realm of strong-field physics, both

experimentally and theoretically. Most theoretical work is hindered by the excessive

computation time, cost, and difficulty of performing calculations on multivalent systems

112

and their behavior within a strong-field. Meanwhile, physical cluster experiments suffer

from a lack of single-target selectivity, limited to working with distributions of clusters

due to the extreme difficulties in performing crossed-beam experiments of this nature.

However, despite this lack of single-target specificity, general observations regarding

cluster species have been made in the past and have led to significant insights into the SFI

behavior of numerous systems.

In the experiments delineated in Chapter 3 of this thesis, it was demonstrated that

the MOCS of the ion products resulting from the SFI of transition metal oxide clusters

followed certain patterns based on their relationship to one another in the periodic table

(those species located in Group Vb or Row 4). It was further shown that this behavior

was related to the energy required to ionize electrons from specific levels of the

constituent atomic cores. Based on the strength of the femtosecond ionization laser

pulse, it was determined that the observed multiply-charged ions were not being created

simply by pure field ionization. On the contrary, the clustered nature of the target species

clearly enhances the ionization behavior observed in the experiments, a phenomenon

which has been demonstrated by many groups on many systems in the past [1-4]. Further

insight was garnered by utilizing extended ionization laser pulse widths, which

demonstrated a lack of collective electron motion (CEM) effects [5] and thus indicated

that the EI mechanisms known as ionization ignition (IIM) [6] and charge-resonance

(CREI) [7] were the most likely sources of EI in those systems.

The specific dynamics behind these two mechanisms has been described in

Chapter 1 and elsewhere in the literature; however, some extrapolation from their

mechanistic implications is necessary to understand the motivation behind the

experiments in this chapter. Regarding the IIM model, the ionization enhancement is

dependent not only on the strength of the external electric field, but also the internal field

associated with the cluster. The localized strength of this internal field is partially

dependent on the total charges of the clustered ions, as well as their internuclear

distances. Thus, by substituting carbon species for the previously studied oxygen

species, the internal field will change, possibly altering the mechanism and the extent to

which ionization progresses. Further, there have been no reported studies which

113

investigate the influences of various heteronuclear species with respect to the CREI

mechanism, which may result in significant changes to the characteristic Rc of the cluster

or simply enhance or retard the ionization process based on the charge, electronegativity,

or location of the clustered ions themselves. In this vein, we present the following

studies on the SFI of various transition-metal carbide cluster species.

Transition metal carbide clusters have been studied for a number of years and

have been a focal point of the experimental and theoretical work performed in the

Castleman group [8-11]. The most well-publicized result was the discovery [12] of the

stable metallocarbohedrene (Met-Car) cluster. Further work in our group has focused on

investigating the electronic, structural, and catalytic properties of the transition metal

carbide cluster family [13,14]. Many of the investigations performed on these species

utilize photoionization and/or photofragmentation techniques which employ nanosecond

lasers as energy sources. To date, the experiments contained within this thesis represent

an initial foray into studies concerning the interaction between ultrashort pulses of strong-

field radiation and the metal carbide cluster family.

Similarly to the transition metal oxide experiments, three sequential metal

species from Row IV in addition to three metals from Group Vb were individually

clustered with carbon and then Coulomb exploded via strong-field radiation.

Observations regarding MOCS values for each set of experiments are provided and

possible implications regarding the ionization behaviors of the clusters with respect to

previous homo- and hetero-nuclear clusters of similar composition are rendered. Due to

the range of cluster sizes and compositions present in the molecular beam, the MOCS

values from each experiment are used for comparisons between species. Specifically,

trends are discovered between carbide clusters containing transition metals from the same

Group or Row. Further, distinctions are drawn between the observed overall

enhancement or restriction of the ionization processes based on presence of oxygen or

carbon within the cluster structures.

114

5.2 Experimental Details

The experimental procedures for these studies have been described in Chapter 2

and thus only a brief summary will be provided here. Strong-field ionization (SFI)

experiments were performed on small transition-metal carbide clusters using a time-of-

flight mass spectrometer (TOF-MS) to observe the MOCS for each cluster distribution as

well as measure pertinent kinetic energy release (KER) data. Clusters were created in a

laser vaporization source by ablating a pure rod of the target transition metal (Ti, V, Cr,

Nb, or Ta) with a focused nanosecond Nd:YAG laser operating at 10Hz. The intensity of

the laser was varied for each species and was adjusted before each experiment to ensure

maximum cluster production within the chosen size distribution. Concomitantly with the

ablation event, a ~300μs pulse of pure methane gas was emitted from a pulsed valve and

directed over the ablation site. The resulting plasma of metal, carbon, and hydrogen

atoms then encountered a small waiting room wherein clustering began before finally

undergoing collisional and expansion cooling while exiting the source via an expansion

nozzle.

For the creation of transition metal carbon clusters, it was imperative that the gas

sample line and mixing tank were flushed with pure methane and then vacuumed out for

at least 5 cycles to minimize the amount of oxygen present in the source assembly.

Further, the stainless steel LaVa source was dissembled and cleaned extensively prior to

experimentation. It was also determined that the oxide layer on the surface of the sample

metal rods was clearly several monolayers thick, and thus for each experiment, the source

was allowed to run for between 1-3 hours with pure methane to eliminate any surface

oxygen on the rod itself. Pure methane (non-diluted) was used as the reactant and

clustering gas, aiding in eliminating the possibility of oxygen contamination within the

individual clusters.

Following formation within the LaVa source, the neutral and ionic clusters then

passed through a 5mm diameter skimmer before reaching the Wiley-McLaren style [15],

two-stage extraction region of the TOF-MS. The apparatus consisted of three

sequentially positioned electrostatic lenses held at constant potentials which were

115

typically +4kV, +2kV, and 0kV, respectively. This gradient provided an excellent

environment to direct the cationic products which resulted from the SFI of the target

neutral clusters into the spectrometer. Further, the proper gradient allowed for sufficient

spatial expansion of the Coulombically exploded ions to enable the measurement of KER

values. The static electric field also ensured that any ionic clusters were deflected and

thus only neutral species were irradiated by the ionizing laser pulse.

Ionization of the transition-metal carbide clusters was achieved via the use of a

colliding pulse, mode-locked (CPM) dye laser which produced pulses of 100fs light

centered at 624nm capable of attaining focused intensities approaching 1x1015

W/cm2.

At this maximum intensity, the incident laser was capable of initiating multiphoton

and/or strong-field ionization within the target clusters, resulting in multiply-charged

ions. These ions were then directed into the TOF-MS where they encountered an Einzel

lens and vertical ion beam steering apparatus used to aim the ions at the microchannel

plate (MCP) detector. As in the previously discussed experiments, two field-free regions

(FFR) were alternately used for data acquisition; a linear 1.3m FFR to resolve KER

splitting and a two-stage reflectron FFR of approximately 3m to attain the highest mass-

to-charge (m/z) resolution possible to alleviate difficulties in species identification. In

several cases, the CPM laser was defocused slightly to minimize multiple ionization

events and highlight the non-Coulomb exploded singly-ionized target clusters to ensure

that the distribution of masses did not exceed the limited range of cluster size which was

the focus of this work.

5.3 Results and Discussion

This section contains the data and discussion related to the SFI experiments on

transition metal carbide clusters. The following figures include several cluster mass

spectra obtained via multiphoton ionization from the defocused CPM beam in addition to

the ion spectra which result from the strong field ionization of the neutral clusters.

116

Further, several tables have been provided to assimilate the data and aid in easing

comparisons between studies.

5.3.1 Titanium Carbide Clusters

Similarly to the spectra obtained from the strong-field ionization of titanium oxide

clusters, the titanium ions in this spectrum are somewhat more difficult to resolve than

others due to several mass-degeneracies with both background contributions as well as

the clustered carbon component (Figure 5-1). In this figure, the x-axis shows the mass-

to-charge (m/z) ratio plotted logarithmically for clarity. The isotope distribution for

titanium is easily recognizable for the +2 charge state. As a result of the unclustered

methane molecules present in the cluster beam, there were significant contributions from

the hydrogenated monocarbon series between m/z = 12 and m/z = 16 as well as in other

sections of the mass spectrum, which added some complexity to the ion identification.

However, titanium ions up to Ti+7

are easily resolvable and the Ti+8

(m/z = 5.9875) and

Ti+9

(m/z = 5.322) species are also present although masked by the large C+2

(m/z =

6.0055) and smaller O+3

(m/z = 5.333) signals, respectively. Further, there is also

evidence pointing to the creation of the Ti+10

ion (m/z = 4.79). However, we were unable

to resolve any higher charge states for the titanium ions; specifically, neither Ti+11

(m/z =

4.355) nor Ti+12

(m/z = 3.992) species were observed. Regarding the carbon species, we

observed that C+1-3

were created not only via SFI of the target clusters, but also from the

background hydrocarbon-based oil species within the chamber. Interestingly though, the

background spectrum reveals little to no evidence of C+4

ions whereas this peak becomes

prominent in the presence of cluster species.

117

The set of 4 sharp peaks on the right side of the C+, C

+2, and C

+3 signals are due to

ringing in the spectrum and do not represent any actual ion signal. The immense signal is

the result of the combined intensity of the carbon ions resulting from the SFI of both the

target clusters as well as the background pump oil which constantly plagued our research.

Care must be taken at all times to closely analyze these types of peaks if they are clearly

present in the same pattern for different species, as this is likely an indication that they

are electronic artifacts and not true signal. Often, the ringing will not be as intense or

even completely absent in the background spectrum due to significantly lower signal

resulting solely from the pump oil. It is imperative that a balance be found between

signal amplification to allow for the observation of the most highly charged ions and

restraining the amplification to minimize ringing and other potential artifacts.

5-1: Mass spectrum of the multiply charged ion species which resulted from the SFI (I~1015W/cm2) of

small titanium carbide clusters. Note the MOCS of Ti+10 and the clear evidence of C+4 in the spectrum.

118

Unfortunately, this spectrum represents a situation in which an ideal compromise could

not be attained. Despite this, metal ions reaching the Ti+10

species are present while there

is also clear evidence of carbon ions reaching the C+4

charge state.

Figure 5-2 contains the reported ionization energy (IE) data from the literature

[16] for the titanium, carbon, and other transition metal species addressed in this work.

The IE values for the corresponding MOCS of each species are listed in bold. Based on

these values, the absence of the C+5

ion is not unexpected, as ~392eV of energy is

required to remove the first electron from the 1s orbital of carbon, which is well in excess

of the deposited energy indicated by the presence of the Ti+10

ion (IE ~ 216eV) and the

absence of the Ti+11

ion (IE ~ 265eV). In fact, the C+5

ion was not produced in any of the

experiments performed, as each cluster appears to have absorbed less than 300eV of total

energy from the external optical field and subsequent laser-cluster interaction

mechanisms. This is discussed in more detail later.

5-2: Reported ionization energy values [16] for the species studied in this chapter. The energy associated

with the MOCS observed in each specific study is highlighted in bold while a box has been provided to

guide the eye to the narrow range of energies corresponding to the MOCS values. All energies are in

electronvolts.

119

We were unable to produce a useful neutral cluster mass distribution spectrum,

but previous work with TixCy cationic clusters produced from our LaVa source

demonstrated a distribution which was limited to species containing fewer than 30 atoms.

Specifically, the Ti8C12+ cluster was shown to exist in massive quantities while smaller

species are significantly lower in population (see Figure A-1 in Appendix A for a

representative spectrum). One caveat in using this particular cationic distribution as a

representation of the currently discussed clusters; the spectrum presented in Appendix A

was produced using a relatively low concentration of methane gas as the clustering

medium (~6% seeded in helium). The current target clusters were created using pure

methane and thus are likely more highly carbonated than the earlier products.

While SFI experiments on homogeneous Tin clusters were not performed, studies

on clusters of titanium oxide were and thus provide the opportunity for interesting

comparisons between the two sets of work. As noted above, the sizes of the neutral

clusters present in the respective molecular beams were assumed to be quite similar and

the intensity of the incident femtosecond laser pulses was reproduced for each

experiment. Remarkably, the MOCS number for the titanium species in each experiment

is identical; Ti+10

was observed for both the oxide studies and the current carbide work.

As noted in the titanium oxide discussion of Chapter 3, as well as here, the identification

of the MOCS for titanium can be quite convoluted due to the nearly identical mass-

degeneracies which exist between highly charged titanium ions and the multiply charged

oxygen and carbon ions which are omnipresent in our experiments. Fortunately, neither

the maximum observed charge state (Ti+10

) nor the lowest unobserved charge state (Ti+11

)

are mass-degenerate with any of the typical background or complementary species,

aiding in the identification of the MOCS in each study.

In Chapter 3, it was experimentally shown that the strong-field ionization

behavior of our heterogeneous transition metal clusters underwent some enhancement

based on their clustered nature. Further, it was demonstrated that this enhanced

ionization (EI) was not the result of collective electron motion effects, which have

previously been shown to play a significant role in SFI of clusters of larger dimensions

[17]. Finally, the observed EI behavior was attributed to a combination of the ionization

120

ignition mechanism (IIM) and the charge-resonance enhanced ionization mechanism

(CREI), the two EI mechanisms typically associated with smaller molecules and clusters

[18]. Thus, the absolute agreement in the MOCS for these two different types of target

clusters is rather intriguing and some interesting conclusions may be drawn. First,

however, the remaining target cluster species will be presented and analyzed.

5.3.2 Vanadium Carbide Clusters

The next transition metal in the row is vanadium and a representative mass

spectrum for the neutral vanadium carbide clusters we studied is provided in Figure 5-3.

The distribution is fairly similar to previously published studies on vanadium carbide

clusters [19], including the relatively more intense signal at m/z~551, corresponding to

the vanadium met-car, V8C12. It has been shown that the relative populations of

vanadium atoms versus carbon atoms can be controlled based on the concentration of the

methane gas being used in the clustering source [13], and thus it is not surprising that our

clusters are highly carborized due to our use of non-diluted methane gas in the cluster

source. The VC2 and V4C6 species have also found to be primary precursors for the

formation of larger clusters [13], and thus their prominent presence is not unexpected.

Also, like the oxygenated and pure metal studies discussed in Chapters 3 and 4, our target

clusters are quite small and contain fewer than 20 atoms. The significantly larger signals

at the lower mass section of the spectrum which correspond to the mono- and di-

vanadium species are likely enhanced by the photofragmentation of larger clusters in the

distribution. This represents an unfortunate downside to procuring neutral cluster

distribution information in this manner; however, the technique still allows for a general

picture of the species present within the cluster beam to be observed and identified.

121

As before, the resolution of the mass spectra containing the cluster distributions

was not specifically controlled by the spatial focusing of our electrostatic lenses, but

relied more heavily on the creation of all the observed ions from a small, finite point

within the ionizing laser field. Regardless, the resolution is more than sufficient to aid in

calibrating the ion distribution. The mass degeneracies for a range of vanadium carbide

clusters can be rather cumbersome without adequate resolution, as the difference in m/z

for one vanadium atom and three carbon atoms is only 3 amu. Differentiation of the

individual species proved not to be an issue, however, as peak splittings representing two

different clusters were easily resolved as shoulders, such as those labeled for the V3C8

and V4C4 species.

5-3: Cluster distribution for neutral vanadium carbide clusters obtained via defocused CPM with an

approximate intensity of 1012W/cm2. Note the enhanced intensity of the Met-Car, V8C12 at mass ~551amu.

The V3C8 and V4C4 peaks are labeled as indicated in the text.

122

Figure 5-4 contains a typical m/z spectrum for the strong-field ionization of these

vanadium carbide clusters. Unlike the TixCy spectrum, these data were obtained using

the long field-free region and thus much of the background signal has been lost due to the

significantly diminished angular resolution implicit in lengthening the flight distance.

Vanadium species possessing up to the +9 charge state are clearly resolved, as is the C+4

ion signal. Similarly to the TixCy experiment, there is no appreciable C+4

signal observed

unless the target clusters are present in the ionization region. Also, the small features at

an approximate m/z of 5.0 are due to imperfect background subtraction and are not the

result of any higher charged vanadium species, specifically the V+10

ion which has a m/z

= 5.0942 . The lack of KER splitting in this particular spectrum is also a result of the

longer field free region.

5-4: Mass spectrum of the multiply charged ion species which resulted from the SFI of small vanadium

carbide clusters. The MOCS for this study was V+9 while C+4 was also easily seen. Dashed lines are

provided to guide the eye and are positioned according to the overall mass-to-charge ratio calibration for

this figure.

123

Like the TixCy and TixCy experiments, a comparison between the previously

performed VxOy cluster studies and the VxCy work shown here yields a remarkably

identical MOCS value for the transition metal: V+9

. Similarly, the non-metal component

of each type of cluster is also ionized up to the 1s orbital. Neither ionization process is

capable of energizing the target clusters to the extent to which the next 1s electrons (O+7

requires ~739eV of energy) can be removed. Based on the lack of the V+10

ion in the

mass spectrum, it is evident that the absorbed energy of the cluster does not exceed

230eV while the presence of the V+9

ion demonstrates that at least 205eV of energy has

been donated. This range of absorbed energy values agrees quite well with those

observed for the titanium studies (see Figure 5-2).

5.3.3 Chromium Carbide Clusters

The maximum metal charge state easily observable in the SFI mass spectrum for

the chromium carbide experiments is the M+8

ion (Figure 5-5). A shoulder on the low

m/z side of the C+2

peak could indicate the presence of Cr+9

(labeled in the figure) while a

low, broad peak at m/z of ~5.26 is likely coming from the background O+3

species. It is

clear that the m/z calibration begins to overestimate the flight time of the smallest m/z

ions and therefore the slightly overestimated m/z assignment for O+3

is most likely the

proper peak assignment. The isotope distribution associated with chromium is clearly

resolved for the +1 and +2 charge states. Again, the highest charged carbon ion is the C+4

species.

124

In comparing the MOCS values for the chromium carbide and chromium oxide

studies, we observe another agreement between the two sets of experiments. The Cr+8

ion is clearly resolvable for both studies while in each case, there is slight evidence for

the production of the Cr+9

ion as well, in the form of a possible shoulder on the left side

of the C+2

peak. This shoulder could, in fact be the result of some KER spreading of the

signal, but this was experimentally irresolvable despite the use of the long FFR and the

large voltage gradient used (designed to minimize the peak splitting) due to the large

amount of energy associated with the KER of carbon from the metal carbide cluster. The

shoulder height is, however, a reasonable expectation for the Cr+9

ion, compared to the

peak intensities of the observed Cr+8+4

species. Further, the energy required for creation

of the Cr+9

ion is a mere 209.3 eV, which is well within the range of energies observed

5-5: Mass spectrum of the multiply charged ion species which resulted from the SFI of small chromium

carbide clusters. Cr+8 is clearly resolved while Cr+9 is likely present, albeit obscured by the large C+2 peak.

Dashed lines corresponding to the overall calibration line are provided to guide the eye and demonstrate the

expected overlap between C+2 and Cr+9 mass signals.

125

for the vanadium and titanium experiments discussed above. On that same note, the Cr+10

ion needs ~244 eV to be formed, which is slightly more than the energies of the

previously identified ions and thus its absence follows from the trends observed thus far.

5.3.4 Niobium Carbide Clusters

Continuing with the approach taken in Chapter 3, now that we have obtained data

regarding the SFI of three consecutive transition metals within the same row, we shall

now present data for clusters containing transition metals within the same group, Group

Vb. Combined with the vanadium carbide data, the following niobium and tantalum

carbide studies will afford excellent opportunity for comparisons and the observation of

trends within the group. Figure 5-6 contains an outstanding representative cluster

distribution for the niobium carbide species investigated here. The majority of these

clusters contain fewer than 21 atoms and, interestingly enough, the neutral Met-Car

(Nb8C12) species is not noticeably enhanced. However, it has been shown in the past that

source conditions can have significant effect on the appearance intensity of the met-car,

and thus this behavior is not unexpected. Of particular note in the spectrum is the

presence of the Nb4C4 species, as it has been found to possess enhanced stability due to

its 2x2x2 cubic structure [20].

126

Figure 5-7 depicts a logarithmically plotted ion spectrum for the strong-field

ionization of small niobium carbide clusters. Metal ions up to Nb+11

are in evidence

while C+4

is the maximum observed charge state for carbon. There is some interference

from the multiply hydrogenated C+ species, but Nb

+8-11 are clear enough to verify the

presence of Nb+6

and Nb+7

which appear as mere shoulders on some of the background

hydrocarbon peaks. Figure 5-8 has been provided to clarify these assignments and

demonstrates the importance of high mass resolution within the experiments and

highlights the utility of employing a reflectron-based long field free region. Creating

narrow peaks with a minimum of peak spreading/splitting allows for the resolution of

narrow shoulders which can aid in the ultimate identification of species with very similar

m/z values. Specifically, in this case CH+ has a m/z = 13.011 while Nb

+7 has a m/z of

13.272, a difference of a mere 0.261amu which is still resolvable within the mass

5-6: Mass spectrum depicting a typical niobium carbide cluster distribution.

127

spectrum. Similarly, Nb+6

= 15.484 while CH3+ = 15.011, yet the transition metal ion

signal is still clearly indicated by the shoulder on the right of the CH3+ peak. In contrast,

the CH2+ peak has no other interfering signals and is manifested as an extremely narrow

peak in the spectrum.

As with the previously discussed cluster experiments, a comparison of the most

highly charged ions observed in each respective spectrum is useful. However, in this

case we can also compare these transition metal carbide cluster experiments to those

performed on homogeneous clusters of niobium atoms. Remarkably, each of these

MOCS values is also in agreement. A comparison between the reported literature value

energies required for the ionization of the 11th and 12

th electrons from a niobium atom is

5-7: Mass spectrum of the multiply charged ion species which resulted from the SFI of small niobium

carbide clusters. The Nb+11 ion is clearly present (dashed lines corresponding to a mass calibration equation are provided). C+4 was also observed, although this spectrum was truncated to highlight the metal

species and thus the highly charged carbon ions are not evident. Figure 5-8 has also been provided to more

clearly demonstrate the identification of the Nb+x (x = 58) species.

128

unfortunately absent. The highest reported value found was that for the Nb+10

ion, which

is approximately 193eV. The energy required to remove the 11th

and 12th

electrons can

be somewhat extrapolated via periodic trends in conjunction with the electron orbitals of

niobium, however.

The removal of the 9th

, 10th, and 11

th electrons from a niobium atom represent the

last 3 electrons taken out of the 4p orbital and thus the energy required to remove each

successive electron from this same orbital will be quite similar. For example, see the

reported energies required for removal of successive electrons from the 3p orbital of both

titanium and vanadium (Table 5-2). For each of these two examples, the increase in

energy required to remove the second and third electron from the orbital is remarkably

similar; a change of ~ 2.2eV for titanium and ~ 1eV for vanadium. Assuming this type of

behavior continues for the niobium species (an assumption which appears to be valid

5-8: Highly truncated mass spectrum resulting from the SFI of niobium carbide clusters. This expanded

view clearly demonstrates the presence of several highly charged niobium species despite near mass degeneracies with several background hydrocarbon peaks.

129

based on the energies required for removal of the first three electrons from the 4p orbital),

we can extrapolate that the energy required to remove the 11th

electron from niobium is

approximately 21eV greater than that for removal of the 10th

electron, which yields an

approximate value of 214eV. This assumed value is also legitimized by the fact that it

falls neatly into the range of energies shown to be absorbed by the previously discussed

examples of titanium, vanadium, and chromium carbide systems. Removal of the 12th

electron from niobium represents ionization of the first electron removed from the more

tightly bound 4d orbital, and thus a large increase in ionization energy is expected, hence

rationalizing the absence of the Nb+12

ion in any of our experiments.

5.3.5 Tantalum Carbide Clusters

The final transition metal carbide study was performed on neutral tantalum

carbide clusters; a mass spectrum of the singly ionized target clusters is shown in

Figure 5-9. As before, the cluster distribution was controlled and limited to those clusters

containing fewer than 20 total atoms. Due to the significantly larger mass of the tantalum

atom (180.95 amu), mass resolution is lost for relatively smaller clusters than the

previously shown studies. Despite the use of undiluted methane gas in the cluster source,

the neutral tantalum carbide clusters show a strong preference for low carbon

substitution, with many of the dominant clusters possessing the same number of carbon

atoms as metal atoms, or in the cases of the lower massed clusters, fewer than their metal

counterparts.

130

The multiply charged ions resulting from the strong-field ionization of these

clusters are shown in Figure 5-10. The MOCS for tantalum is the Ta+11

ion while C+4

is

clearly present as the highest charged carbon species. Unfortunately, the ionization

energy data provided from the literature [16] is even more truncated for tantalum atoms

than it is for niobium and values were only found for species up to the Ta+5

ion.

However, the general trend down the periodic table for ionization energies is that the

larger the mass of the atom within a specific group, the lower its respective outer electron

valence energies are typically found to be. This is exemplified in the pattern manifested

for the first 5 ionization energies of the Group Vb elements as shown in Figure 3-12 in

Chapter 3. Further comments regarding this trend may also be found there. Thus,

subsequent discussion regarding the appearance energy for the highest charged tantalum

ions would be very involved and thus will not be expounded upon here.

5-9: Typical mass spectrum of the target tantalum carbide cluster distribution. Mass resolution becomes

decreased around 960 mass units but the observed stoichiometry is still identifiable.

131

Like the niobium experiments, these tantalum carbide studies may also be

compared to not only the tantalum oxide work but also the ionization observed for the

homogenous tantalum clusters. Again, we observe identical MOCS values for each

different type of cluster distribution, with ionization reaching a maximum of Ta+11

.

However, unlike the pure tantalum studies, the possibility of higher charge states cannot

be simply ruled out based on the observed species in the mass spectrum. As noted in the

Chapter 3 discussion of higher Ta+x

ion identification, the next few tantalum ions are

nearly exactly mass-degenerate with several other species which are likely present in the

mass spectrum. Specifically, Ta+12

(m/z = 15.079) and CH3+ (m/z = 15.011), Ta

+13 (m/z

= 13.9191) and CH2+ (m/z = 14.011), Ta

+14 (m/z = 12.9249) and CH

+ (m/z = 13.011), and

finally Ta+15

(m/z = 12.0132) and C+ (m/z = 12.011) are all nearly degenerate and thus

their presences cannot be confirmed nor denied. However, the extremely small intensity

5-10: Mass spectrum of the multiply charged ion species which resulted from the SFI of small tantalum

carbide clusters. The maximum charge states of Ta+11 and C+4 are evident.

132

of the Ta+11

signal may yield some indication that it is quite possibly the highest charge

state created within these experiments. Signals of lower intensity may simply be

irresolvable, despite any signal overlap due to mass degeneracy. Thus, we observe a

continuation of the trend discussed above, in that regardless of overall cluster

composition within a finite distribution of species, the EI processes involved in the SFI of

the target systems yield very comparable, if not identical, maximum charge states for any

given species.

The maximum observable charge states for each of the constituent atoms

composing the cluster species studied herein are delineated in Table 5-1. As noted above,

the MOCS trends discovered for the transition metal oxide studies (Chapter 3) and

homogeneous transition metal cluster studies hold true in the carbide systems. Indeed,

the SFI of clusters composed of transition metals and carbon results in the removal of

electrons well beyond the valence shell of the constituent metal atoms while being

capable of stripping the entire valence shell of the carbon species. Further, it is evident

that field ionization alone cannot account for the highly multiply charged ions observed

in the mass spectra, as the ponderomotive potential of the incident electric field is again

less than 40eV at its peak, from which the maximum charge states possible would be M+4

and C+2

. Thus, although the basic mechanisms governing the EI within these clusters has

already be discussed at length in Chapters 3 and 4, some further discussion regarding the

expected ionization behaviors of each type of system based on composition is

worthwhile.

133

These transition metal carbide clusters provide an excellent opportunity for

comparison with the transition metal oxide clusters discussed in Chapter 3. The impact

of cluster properties between the transition metal oxide species and their homonuclear

counterparts were well covered in Chapter 4, but here we are presented with an

opportunity to compare much more similar species, in that they are both heterogeneously

composed of transition metals and more electronegative species. Further, each class of

cluster (oxide or carbide) possesses polar covalent bonds and the consequential increase

in structural rigidity (compared to clusters of a purely metallic nature) which

accompanies this type of bonding scheme. Thus, we can compare the ionization

behaviors of similarly composed cluster distributions in which the highly electronegative

oxygen components have been replaced by the less electronegative carbon atoms.

Based on the principles involved in the ionization ignition model of enhanced

ionization, it is rather remarkable that the influence of the maximum charge state of the

non-metallic component of the clusters appears to be insignificant. Specifically, at its

highest charge state, the carbon atoms within the cluster reach a +4 ionization state,

which oxygen atoms were observed to reach the +6 state. This change in charge was

expected to have a noticeable difference in influencing the interior electric field

landscape of the target clusters, leading to a less significant impact on the lowering of the

5-1: Overall summary of the maximum observed charge states resulting from the strong-field ionization

of several transition metal oxide, carbide, and homogenous clusters. The (+9) attributed to the chromium

species is likely present, as discussed in the text.

134

ionization energy of the transition metals and thus the creation of fragments possessing

less complete ionization. However, this is clearly not the case, as each experiment

regardless of transition metal identity resulted in the observation of identical MOCS

values regardless of non-metallic component (or the lack thereof, in the homogenous

studies of niobium and tantalum).

In Chapter 4, where it was shown that heteronuclear transition metal oxide and

homonuclear transition metal clusters under similar SFI conditions yielded identical

maximum charge states, some discussion was offered with regard to possible scenarios

which would lead to this similar ionization behavior. Specifically, it was hypothesized

that the structural motif of the transition metal oxide clusters, in which the metal ions are

typically located in the interior part of the cluster while the oxygen components are often

positioned at either bridging or terminal positions on the relative exterior of the cluster,

might lend itself to less significant CREI ionization between the metal and oxygen atoms

due to the rapid emission of the lighter oxygen species while further ionization

enhancement occurred between the more massive, and thus slower expanding, metallic

nuclei. Given the concomitant lack of change in MOCS values when carbon is

introduced as the clustering counterpart, this hypothesis may be further supported.

Regardless of whether the cluster is composed of pure transition metal, metal and

oxygen, or metal and carbon, the SFI of each system results in the same highly charged

metal ions. Thus, perhaps the most significant ionization enhancement occurs

specifically between the transition metal atoms themselves while the carbon and/or

oxygen atoms participate to a lesser extent.

135

Upon studying the calculated structures of typical transition metal carbide

clusters, however, we find a distinct departure from the structural motifs associated with

transition metal oxide clusters. For instance, as shown in Figs. 5-6 and 5-9, many of the

observable transition metal carbide clusters for niobium and tantalum, respectively,

contain similar numbers of metal and carbon atoms. This has previously been reported in

the literature and thus numerous attempts to calculate structures using similar

stoichiometries have been undertaken. Several examples from previous work [21] are

provided in Figure 5-11. As clearly evidenced in these calculations, the transition metal

carbide species do not typically adopt structures in which the metals are more centrally

located while the non-metallic species are found closer to the exterior of the structure.

The structures appear to favor more evenly distributed motifs reminiscent of the

previously mentioned 2x2x2 cubic structure associated with the M4C4 cluster. Further,

for the more highly carborized species (see examples of TixCy [22] in Figure 5-12) tend

5-11: Theoretically calculated structures for NbxCy clusters [21].

136

towards more cage-like structures, a further departure from the typical pattern found for

transition metal oxides. However, despite the overall differences in structural motif, one

cannot rule out the possibility for interaction between the metallic species within the

clusters and thus it is still quite feasible that the metal-metal interactions are dominant in

the EI mechanisms therefore resulting in similarities in ionic charging observed in our

experiments, regardless of overall cluster composition.

5-12: Theoretically calculated structures of several TixCy clusters [22].

137

5.4 Conclusions

In conclusion, we have performed SFI experiments on a variety of transition

metal carbide clusters which resulted in the enhanced ionization of the target systems

well beyond the charge states possible based purely on field ionization via the incident

laser pulse alone. We have observed and explained trends regarding the maximum

observable charge states for each type of cluster. Further, the results of these transition

metal carbide experiments were compared to those reported for pure transition metal

clusters and transition metal oxide clusters and complete agreement between MOCS

values for each species of transition metal was discovered. The lack of influence of

cluster composition in the observable ionization enhancement of the target clusters is

quite unexpected.

It has been shown throughout the literature that ionization is enhanced for clusters

in the presence of a strong laser field, but until the systematic and widely-encompassing

work presented here, the influence of cluster composition has been a largely unexplored

area of this field. We have found that in each of the clusters targeted, a remarkably

similar amount of energy was required to produce the observed high charge states for the

transition metals composing them. Thus, it can be concluded that the complex radiation-

matter interaction, including the Stark-shifting of electronic orbitals as a result of the

laser field, the ionization barrier suppression due to neighboring ionic nuclei within the

cluster, and the superposition of the external electric field with the cluster’s internal

potential landscape, results in an environment in which transition metal ions of various

identities but strikingly similar ionization energies are created and observed.

It is important to remember that each of these experiments was performed on a

range of clusters composed of a variety of different atomic ratios, total atomic numbers,

as well as cluster structures and that all of these observations are the result of a

culmination of ionization behavior over the entire cluster distribution. It is for this reason

that we have concentrated on the maximum observable charge state created from the SFI

of each system. By focusing on the maximum charge states, we hoped that any

significant change in ionization behavior would be manifested throughout the cluster

138

distribution and thus would be observable as a change in the MOCS for each type of

cluster system. Further experimentation on mass-selected clusters would be ideal in a

continuous effort to ascertain the structural dependence of the intriguing phenomena

which play such an important role in the strong-field ionization of small molecules and

clusters.

139

5.5 References

[1] Snyder, E.M., Wei., S., Buzza, S.A., Castleman Jr., A.W., Chem. Phys. Lett., 248 (1-

2), 1-7 (1996).

[2] Purnell, J., Snyder, E.M., Wei, S., Castleman Jr., A.W., Chem. Phys. Lett. 229 (4-5),

333-339 (1994).

[3] Snyder, E.M., Buzza, S.A., Castleman Jr., A.W., Phys. Rev. Lett., 77 (16), 3347-3350

(1996).

[4] McPherson, A., Thompson, B.D., Borisov, A.B., Boyer, K., Rhodes, C.K., Nature,

370 (6491), 631-634 (1994).

[5] McPherson, A., Luk, T.S., Thompson, B.D., Boyer, K., Rhodes, C.K., Appl. Phys. B.,

57, 337 (1993).


1182-1190 (1997).


[8] Castleman Jr., A.W., Bowen Jr., K.H., J. Phys. Chem., 100, 12911 (1996).

[9] Wei, S., Guo, B.C., Purnell, J., Buzza, S., Castleman Jr., A.W., J. Phys. Chem., 96

(11), 4166-4168 (1992).

[10] Guo, B.C., Kerns, K.P., Castleman Jr., A.W., JACS, 115 (16), 7415-7418 (1993).

[11] Cartier, S.F., May, B.D., Castleman Jr., A.W., J. Phys. Chem., 100 (20), 8175-8179

(1996).

[12] Guo, B.C., Kerns, K.P., Castleman Jr., A.W., Science, 255 (5050), 1411-1413

(1992).

[13] Knappenberger, K.L., Jones, C.E., Sobhy, M.A., Iordanov, I., Sofo, J., Castleman Jr.,

A.W., J. Phys. Chem. A, 110 (47), 12814-12821 (2006).

[14] Knappenberger, K.L., Clayborne, P.A., Reveles, J.U., Sobhy, M.A., Jones, C.E.,

Gupta, U.U., Khanna, S.N., Iordanov, I., Sofo, J., Castleman Jr., A.W., ACS NANO, 1 (4),

319-326 (2007).

[15] Wiley, W.C., McLaren, I.H., Rev. Sci. Instrum. 26, 1150 (1956).

140

[16] CRC, Handbook of Chemistry and Physics, 89th Ed., 2008/09, editor D. Lide,

Cleveland, OH: CRC Press, p. 10-203/205.


K.H., Phys. Rev. Lett., 82 (19), 3783 (1999).


R77 (2006).

[19] see, for e.g., Brock, L.R., Duncan, M.A., J. Phys. Chem., 100 (14), 5654–5659

(1996).

[20] Yeh, C.S., Byun, Y.G., Afzaal, S., Kan, S.Z., Lee, S., Freiser, B.S., Hay, P.J., JACS,

117 (14), 4042-4048 (1995).

[21] Harris, H., Dance, I., J. Phys. Chem. A, 105 (13), 3340-3358 (2001).

[22] Munoz, J., Rohmer, M.M., Benard, M., Bo, C., Poblet, J.M., J. Phys. Chem. A, 103

(24), 4762-4768 (1999).

Appendix A

Useful Equations

Laser Intensity

Where I = intensity, E = energy of the unfocused laser (joules), Γ is the pulse width in

seconds

Focused laser beam radius

Where r = radius of focused beam, f = focal length in mm, λ = wavelength in nanometers,

D = prefocused beam diameter

Keldysh (adiabatic) Parameter

Where γ = Keldysh (adiabatic) parameter is unitless, Ip = ionization potential of the

atom/molecule/cluster in eV, Up is the ponderomotive potential in eV of the femtosecond

pulse

142

Ponderomotive Potential (electron quiver energy)

Where Up is the ponderomotive potential (or quiver energy) in eV, Ip is the laser intensity

at its focus in PW/cm2 (PW = 10

15W), and λ is the central wavelength of the laser in

nanometers. 9.33738*10-5

is a constant used as a unit correction.

Power conversion from Molectron Power Meter

Where V = number of volts read on the oscilloscope with the Molectron power meter in

short pulse mode and the oscilloscope terminated with 1Mohm resistance.

Kinetic Energy Release (KER)

Where KER is in eV, q is the charge of the ion, is the difference in TOF for the peak

of the forward and backward ejected species in microseconds, m is the mass of the

species, U1 is the voltage on the repeller plate, U2 is the voltage on the extractor plate,

and d is the distance between the repeller and extractor plates in centimeters.

Effective Nuclear Charge (Qeff)

when

143

Or

when

Where ra is the SCF function atomic radius and Z is the atomic number.

VITA

Daniel Edward Blumling

Born on December 30, 1980 in Virginia Beach, VA, Daniel Edward Blumling is

the oldest of three sons begotten by his parents, Robert Alan Blumling and Georjeane

Linley Blumling. After graduating from Catholic High School (now known as Bishop

O’Sullivan Catholic High School) of Virginia Beach, VA in 1998, he went on to earn his

Bachelor’s Degree in Chemistry from Mary Washington College (now known as the

University of Mary Washington) in Fredericksburg, VA. Following graduation, he

performed his doctoral dissertation work at the Pennsylvania State University in

University Park, PA under the tutelage of Professor A.W. Castleman, Jr. and earned his

Doctor of Philosophy degree in Chemistry in the winter of 2009. At the time of this

publication, he is a postdoctoral associate at Florida State University working for Dr. Ken

L. Knappenberger. Daniel lives in Tallahasse, FL with his wife, Michelle.

STRONG-FIELD IONIZATION STUDIES OF HOMO- AND …

Documents

Transcript of STRONG-FIELD IONIZATION STUDIES OF HOMO- AND …